Alexander Iosevich

Department of Mathematics

University of Rochester

Last updated: September 30, 2023

__Contents:__

__Personal Information__

__Education__

__External Funding__

__Positions Held__

__Research Interests
News articles
Practical skills
__

Editorial Board Membership

Selected invited talks

Elementary/High school student mentoring

__Email: __iosevich@math.rochester.edu

__Date of Birth:__ December 14,
1967

__Citizenship:__ United States of
America

June 1993, Ph.D. in Pure Mathematics,
University of California at Los Angeles (UCLA)

Thesis: *"Maximal operators
associated to families of flat curves and hypersurfaces"*

* *Advisor: Christopher Sogge

June 1989, BS in Pure Mathematics, University of Chicago

**Awards and Honors: **

AMS
Fellow, Class of 2014

Professor
of the Year Award in the Natural Sciences, University of
Rochester, 2015

Analysis, Grant Number DMS97-06825 Amount: $53,000

March 2000, United States National Science Foundation Grant in Classical (PI)

Analysis, Grant Number DMS00-87339 Amount: $77,000

March 2003, United States National Science Foundation Grant in Classical (PI)

Analysis, Grant Number DMS02-45369 Amount: $114,000

June 2005, United States National Science Foundation Collaborative Research Grant (PI)

Analysis, Grant Number DMS04-56306 Amount: $474,245

August 2009, United States National Science Foundation Grant in Number Theory (PI)

and Algebra, Grant Number DMS10-45404 Amount: $303,000

April 2015, United States National Science Foundation Conference Grant (PI)

for the ICHAA conference at the CUNY Graduate Center Amount: $50,000

May 2015 United States National Security Agency Grant H98230-15-1-0319 (PI)

in Combinatorics. Amount: $120,000

November 2019 HDR TRIPODS (NSF): Collaborative Research: Foundations of Greater Data Science (co-I)

Amount: $814,165

March 2022 NSF DMS 2154480: International Conference on Microlocal Analysis, Harmonic Analysis and Inverse Problems

Amount: $36,171

June 2022 NSF DMS 2154232 On problems and connections between analysis, geometry and combinatorics

Amount: $322,800

July 1, 2010-Present, Professor of
Mathematics, University
of Rochester, Rochester, NY

September 1, 2005-May 31, 2010, Professor of Mathematics, University of
Missouri-Columbia, Columbia, Missouri

January 1, 2008-July 31, 2008, Visiting Faculty and Program
Organizer, Fields Institute of Mathematics, Toronto, Canada

September 1, 2002 to August 31, 2005, Associate Professor in
Department of Mathematics, University of
Missouri-Columbia,

Columbia, Missouri

July 2000 to September 2002, Assistant
Professor in Department of Mathematics, University of
Missouri-Columbia, Columbia, Missouri

May 2000 to April 2001, tenured
Associate Professor in Department of Mathematics,

Georgetown University,
Washington, District of Columbia

July 1998 to May 2000, Assistant
Professor in Department of Mathematics,

Georgetown University,
Washington, District of Columbia

Summer 1999, University of Illinois at
Chicago, j*oint research with N. Katz facilitated by a CRB
Grant.*

September 1995 to December 1998,
Assistant Professor in Department of

Mathematics, Wright State University,
Dayton, Ohio

June/July 1998, Visiting Research
Fellowship, University of New South Wales, Sydney, Australia.

Fall 1997, General Membership at the
Mathematical Sciences Research Institute, Berkeley, California

September 1993 to September 1995,
Postdoctoral Fellow, McMaster
University,

Hamilton, Ontario, Canada

September 1989 to September 1993,
Graduate Student, Teaching Assistant and

Research Fellow, UCLA, Los Angeles,
California

Harmonic Analysis and Geometric Measure Theory

Data Science and Neural Networks

Additive Number Theory and Discrete Geometry

Analytic Number Theory

"Nasty"
geometry breaks decades-old tiling conjecture - Quanta
magazine article

"Why
this Rochester math professor champions year-round
undergraduate research" - University of Rochester News
Center article

"Doctor's
advice"- Careers magazine article about job search for
Ph.Ds.

"UR's
Covid-19 budget cuts lead to faculty frustrations" -
University of Rochester, Campus Times article

"Mathematics
students gain retail analytics experience through Parker Avery
partnership" - Parker Avery Group podcast

Python, Maple, Machine Learning, Reinforcement Learning, Sales Forecasting Models, Technical Documentation

Ryan Mullen (Masters 2002) Prognos Inc.

Daniel Weidinger (Masters 2003) SETA Test Scientist at Shafer
Corporation

George Arutunyants (Ph.D. 2006) The head of analytics at Prognos
Inc.

Derrick Hart (Ph.D. 2008) Assistant Professor of Mathematics

Doowon Koh (Ph.D. 2008) Associate Professor of Mathematics at
Chungbuk University, Korea

Janet Sipes (M.S. 2009) Arizona State University (graduate
student)

Hannah Morgan (M.S. 2009) University of Chicago (graduate
student)

Jeremy Chapman (Ph.D. 2010) Associate Professor of Mathematics
at Lyons College, Arkansas

Steven Senger (Ph.D. 2010) Assistant Professor of Mathematics at
the Missouri State University

Le Anh Vinh (Ph.D. 2011) Professor at the University of Hanoi

David Covert (Ph.D. 2011) Assistant Professor of Mathematics at
the University of Missouri-St. Louis

Krystal Taylor (Ph.D. 2012) Assistant Professor of Mathematics
at the Ohio State University

Esen Aksoy (Ph.D. 2014) Texas A&M University in Qatar

Mike Bennett (Ph.D. 2015) Visiting
Assistant Professor at the Rochester Institute of Technology

Dillon Ethier (Ph.D. 2016) Seeking employment in statistical
consulting industry

Brendan Murphy (Ph.D. 2016) Heilbron Postodoctoral Researcher at
the University of Bristol

Bochen Liu (Ph.D. 2017) Postdoctoral Resercher at Bar-Ilan
University, Israel

Philipp Birklbauer (Ph.D. 2019) Computer programmer in Chicago,
Illinois

Dionel Jamie (Masters 2019) Ph.D. student at the University of
Wisconsin-Madison

Nik Chatzikonstanti (Ph.D. 2020) Posdoctoral Researcher at the
Okinawa Institute of Technology

Jonathan Passant (Ph.D. 2021) Heilbron Postdoctoral Researcher
at the University of Bristol

Alex McDonald (Ph.D. 2021)
Postdoctoral researcher at Ohio State University

Belmiro Galo (Ph.D. 2021) Visiting Assistant Professor of
Mathematics at Colgate

Brianna Vick (Ph.D. 2021) Assistant
Professor of Mathematics at Clayton University

Gail Jardine (Ph.D. 2022) Defense Contractor, Virginia

Tingsong Jiang (Ph.D. 2022) Seeking a position in Big Data

Tritium Shen (Ph.D. 2022-expected) Data Science internship,
Houston, TX

Shashank Chorge (Ph.D. 2023)
Postdoctoral researcher at IIT

Brian McDonald (Ph.D. 2023) Postdoctoral
researcher at UGA

Anirudh Gurjale (Ph.D. 2022-expected)

Firdavs Rakhmonov (Ph.D. 2023-expected)

Shashank Chorge (Ph.D. 2023-expected)

Donggeun Ryou (Ph.D. 2024-expected)

Pablo Bhowmick (Ph.D. 2025-expected)

Shengze Duan (Ph.D. 2025-expected)

Quy Pham (Ph.D. 2026-expected)

The following is the list of students who
completed an undergraduate honors thesis under my direction.

Xiaoqing Tang (2012) Microsoft

Emmett Wyman (2014) Johns Hopkins
University (graduate student in mathematics) and now a postdoc
at Rochester

Yujia Zhai (2014) Cornell University (graduate student in
mathematics) and now a postdoc at Bordeaux

Luke Vaicunas (2015) Parker Avery

Brian McDonald (2016) University of
Chicago (graduate student) and now a graduate student at
Rochester

Lisa Rosenfeld (2016) FDIC Pittsburgh

Adam Scrivener (2016) Epic Systems, Madison, WI

Ben Dees (2017) Johns Hopkins University, Baltimore, MD
(graduate student in mathematics)

Daniel Rubery (2017) Google

Adam Lott (2017) University of California Los Angeles (graduate
student in mathematics)

David Soukup (2018) University of California Los Angeles
(graduate student in mathematics)

Dionel Jaime (2018) University of Wisconsin (graduate student in
mathematics)

Zhonghui Sun (2018) Michigan State University (graduate student
in mathematics)

Manuel Stoeckl (2019) Dartmouth University (graduate student in
computer science)

Zachary Polansky (2019) Google

Byron Osterweil (2020) University of California-Irvine (graduate
student in mathematics)

Dustin Kasser (2020) University of Georgia (graduate student in
mathematics)

Linus Ge (2021) Ohio State University (graduate student in
mathematics)

Xiaobo Luo (2021) Harvard University (graduate student in data
science)

Yiyang Su (2021) Michigan State University (graduate student in
computer science)

Mandar Juvekar (2022-Expected) Boston University (graduate
student in computer science)

Arian Nadjimzadah (2022-Expected) UCLA
(graduate student in mathematics)

Conor Taliancic (2022) Taking a gap year

Nathan Whybra (2022) Computer programmer

Thomas O'Neill (2022) Taking a gap year

Cierra Tinson (2022) Michigan State University (graduate student
in physics)

Michele Martino (2022) University of Washington (graduate
student in applied math/data science)

Filippo Iulianelli (2022) University of Pennsylvania (graduate
student in physics)

Anna Myakushina (2023) University of Maryland (graduate student
in statistics)

Livia Betti (2023) Taking a gap year

Yakun Yang (2023) University of Michigan (graduate student in
statistics)

Yun Long Xu (2023) University of Chicago (graduate student in
neuroscience)

Rachel Dennis (2023) Newgrange design (PCB designer)

Elana Elman (2024)
(expected)

Peter MacNeil (2023) (expected)

**Research
programs for undergraduate students
**

**2002-2010: **Informal
summer research programs for undergraduate students at the
University of Missouri.

**2011-Present:** Informal summer research programs for
undergraduate students at the University of Rochester and
neighboring colleges and universities.

**2018-Present:** StemForAll summer research program at the
University of Rochester with special emphasis on participants
who are women and members of underrepresented groups.

**2019-2023:** NSF Tripods Research Program in mathematical
methods in data science with special emphasis on
participants who are women and members of underrepresented
groups.

**2021-Present:** Year-round undergraduate research program
in applied and theoretical aspects of data science

CIMPA
workshop on analysis and probability in Armenia, July 2024

International Conference on Microlocal
Analysis, Harmonic Analysis and Inverse Problems, August 2022

CIRM
(Luminy) workshop on geometric measure theory, ergodic theory
and combinatorics, January 2021

ICERM
workshop on Frame Theory and Exponential Bases, June 4-8,
2018

Excelsior Lectures in Analysis, with L. Lanzani, September 2017
at Syracuse University.

Excelsior Lectures in Analysis, with
L. Lanzani, September 2016 at the University of Rochester.

International
Conference on Harmonic analysis and Applications, with A.
Mayeli and G. Olafsson, June 2015.

AMS Special Session, Rochester, NY, special session in memory of
Daryl Geller, with A. Mayeli.

Fields Institute Program, entitled "Trends in Harmonic
Analysis", January 1- June 30, 2008, (with I. Laba, M. Lacey,
and E. Sawyer).

AMS Special Session, Davidson, North Carolina, March 2007 (with
M. Lacey and K. Oskolkov).

AMS Special Session, Salt Lake City, Utah, October 3-5, 2006
(with M. Lacey).

Combinatorial and
additive number theory (CANT 2005). A conference in
celebration of Mel Nathanson's 60^{th} birthday. (Member
of the organizing committee).

CMS conference at Simon Fraser
University in Vancouver (with I. Laba), December 6-8, 2003.

ESI
(Schrodinger Insitute in Vienna) Workshop on mathematics
related to the Kakeya Needle Problem, (with I. Laba and D.
Muller), Vienna, Austria, Fall 2003.

A conference
on Harmonic Analysis and Partial Differential Equations at
the University of Missouri, May 8-11, 2002, (with L. Grafakos,
S. Hofmann, and I. Verbitsky).

Workshop
on convexity and Fourier analysis, (with L. Brandolini, L.
Colzani, and G. Travaglini), Milan, Italy, June 2001.

In 2008, Izabella Laba, Sinai Robins and I
launched a new journal- Online Journal of Analytic
Combinatorics, or OJAC for short. The current managing editors
of the journal are Eyvindur Palsson and Steven Senger. The
current advisor board consists of Alez Iosevich, Sinai Robins
and Steven Senger. Please check out the OJAC web page at http://www.analytic-combinatorics.org/index.php/ojac

Journal
of Pseudo-Differential Operators and Applications 2008-Present

Harmonic
analysis editor of the Proceedings of the American
Mathematical Society 2011-January 2020

Member
of the editorial board of the Journal of Fourier Analysis and
Applications 2016-Present

Carus Manuscripts (MAA) Editorial Board January 2017-Present

Integers
Journal Editorial Board October 2016-Present

Fractals
and Fractional Editorial Board 2021-Present

Research
in Mathematical Sciences Editorial Board 2022-Present

Associate Editor of the Canadian Mathematical Society
Publications Committee, 2023-Present

Associate Editor of the Canadian Journal of Mathematics,
2023-Present

Associate Editor of the Canadian Mathematical Bulletin,
2023-Present

__Selected
educational and administrative activities:__

Member of the Best Paper in the Mathematical
Society panel established by the City of Beijing and executed by
the Yanqi Beijing Institute of Mathematical Sciences and
Applications

Associate Editor of the Canadian Mathematical Society
Publications Committee, 2023-2025

Member of the University of Rochester AAUP Chapter, July
2020-Present.

Meliora Committee (advisory committee to the Chair of the
Department of Mathematics) August 2019-April 2020.

Committee on salary gender equity, University of Rochester,
member, September 2018-May 2019.

GradStemForAll summer program with emphasis on women and
underrepresented groups, 2018-Present.

American Engagement Network, member, April 2018-Present.

AQUAD Review University of Massachusetts-Boston, March 2018.

Mentored Allen Liu, an Intel High School Science Competition
Finalist, 2016.

The Classical Analysis moderator for arxiv.org, September
2014-2021.

Member of the Math Arxiv advisory committee, April 2014-Present.

Summer research program for
undergraduate students at the University of Rochester,
June-August 2011-Present.

Director of Graduate Studies at the University of Rochester
Department of Mathematics, January 2010-August 2014.

Member of the AMS Committee on Meetings and Conferences, January
2009-April 2012.

Summer program for high school students on Fourier analysis in
finite fields at the University of Missouri, July 24-28, 2006.

Campus Writing Program's Fall 2005 Faculty Workshop.

Summer
program
for high school students on the Erdos distance problem at the
University of Missouri, August 1-5, 2005.

Putnam coach, University of Missouri-Columbia, 2000-2009.

MU McNair scholars program- departmental liason, 2004-2010.

Summer
program for high school students on geometric combinatorics at
the University of Missouri, August 9-13 2004.

Volunteer for the 2004 MAA High School Lectureship Program.

Faculty mentor for the University of
Missouri summer minority outreach program, Summer 2003, mentor
for Ivy Hunter.

Participant
in the Teaching Renewal Conference at the University of
Missouri 2002.

Member of the Judge Panel of the 2000
USA College Academic Team. Sponsored by USA TODAY, 2000.

High School Outreach Program,
sponsored by Wright State University, 1996.

Volunteer tutor, Bret Harte Elementary
School, Chicago, Illinois, 1986.

**Elementary/High
****s****chool student mentoring:**

Tyler Jones-Salisbury (2005-2009)

Allen Liu (2014-2017)

Davey Fitzpatrick (2015-2018)

Ty Lewis (2020-2021)

Noah Lee (2019-2020)

Maxwell Sun (2019-2022)

Kevin Xue (2021-2022)

Amy Fang (2021-2022)

Surya Ramkumar (2022-Present)

Professor
of the Year Award in the Natural Sciences, University of
Rochester, 2015

Nominated for the University of
Missouri Kemper Award for Excellence in Teaching, 2008 and 2009.

Nominated for Provost's Outstanding Junior Faculty Teaching
Award, University of Missouri, 2003

Wolper's house teaching award,
University of Missouri, 2001.

Wright State University Athletics
Department Award, 1997.

Wright State University Athletics
Department Award, 1995.

Nominated for Undergraduate Student
Government Teaching Award at McMaster University, 1994.

**Selected Invited
Talks**

January
2023 An invited plenary lecture at the Renyi Institute
conference on Fourier Analysis and Additive Problems

Title: Uniform distribution and pseudo-randomness

July 2023 An invited plenary talk at the 1st International Forum
in Basic Science, Beijing, China

Title: Graphs and multi-linear operators

April 2023 An invited Pi Mu Epsilon Lecture at the University of
Nebraska-Lincoln

Title: From analysis to combinatarics to number theory and
back

March 2023 An invited plenary talk at Harmonic Analysis and
Fractal Sets Conference at the Ohio State University

Title: Fractal analysis and complexity theory

February 2019 A plenary lecture at the Weitzmann Institute
Conference in honor of Alexander Olevskii

Title: Geometric measure theory and applications to frame
theory

September 2018 A plenary lecture at the 7th International
Conference "Harmonic Analysis and Approximation", Armenia

Title: Finite point configurations and frame theory

February 2018 A lecture series on the Falconer Conjecture at the
Louisiana State University

Title: Falconer distance conjecture and applications to
functional analysis

September 2017 A plenary lecture at the conference at the
University of Wroclaw in honor of Eli Stein

Title: Finite point configurations, Hausdorff dimension
and rigidity

October 2016 A plenary lecture at the Integers Conference in
Georgia

Title: Geometric configurations in vector spaces over
finite fields

September 2016 A keynote address at the combinatorial geometry
conference in Hanoi, Vietnam

Title: Analytic, combinatorial and number theoretic
methods in the study of finite point configurations

May 2015 A plenary lecture at the Complex Analysis and Dynamical
Systems VII conference in Nehariya, Israel

Title: The Fuglede Conjecture holds in two dimensional
vector spaces over prime fields.

August 2012 A lecture series at Chungbuk University, South Korea

Title: Multi-linear bounds and applications to geometric
measure theory and combinatorics

March 2012 An invited lecture at the
analysis seminar at Princeton University

Title: Distribution of simplexes in discrete and
continuous settings and multi-linear operators

June 2011 An invited lecture at the Edinburgh Workshop on
Harmonic Analysis

Title: Geometric consequences of analytic inequalities

September 2008, An invited lecture at the Oberwolfach (Germany)
meeting on Discrete Geometry

Title: Geometric configurations in Euclidean, integer and
finite field geometries: combinatorial and algebraic aspects

July 2008, An invited lecture at the
Oberwolfach (Germany) meeting on Harmonic Analysis

Title: Geometric configurations in Euclidean, integer and
finite field geometries

April 2008, An invited lecture at the
Fields Institute (Toronto, Canada) Conference on Additive Number
Theory

Title: Distribution of dot products in vector spaces in
finite fields and applications to problems in additive number
theory and geometric combinatorics

October 2007, A plenary address to the
American Mathematical Society at DePaul University, Chicago

Title: Incidence theory: discrete, continous and
arithmetic aspects

March 2007, A plenary address to the
American Mathematical Society at Davidson College, North
Carolina

Title: Incidence theory: discrete, continous and
arithmetic aspects

November 2006, A lecture series on
harmonic analysis at the University of Bristol (four lectures)

Title: Harmonic analysis in vector spaces over finite
fields

May 2006, CUNY, New York, CANT 2006 (three lectures)

Title: "Three lectures on analytic, combinatorial and
number theoretic aspects of incidence theory"

May 2003, Princeton University
Analysis Seminar

Title: Combinatorics of distance sets and applications

April 2003, Riviere-Fabes Symposium in
Analysis

Title: Analysis and combinatorics of distance set

March 2003, The Erwin Schrodinger
International Institute (Vienna, Austria) for Mathematical
Physics

Title: Analysis and combinatorics of distances sets

June 2002, University of Padova
(Padova, Italy), Minicorsi di Analisi Matematica (three
lectures)

Title: "Geometric combinatorics and applications to
analysis"

**I nvited Talks and
Research Stays:** (385 lectures and 33 lectures from
11 lecture series)

__C____ount____ries:__ Argentina,
Armenia, Australia, Austria, Canada, Catalonia, Czech Republic,
China, England, Finland, France, Germany, Greece, Hungary,
Israel, Italy, Poland, Russia, Scotland, Spain, Ukraine,
Vietnam, Wales.

**2024 **(385)

June 9-14, 2024 An invited
lecture at the Banff conference, On the interface of geometric
measure theory and harmonic analysis

Title: Applications of geometric measure theory to large
data

March 5-7, 2024 An invited plenary lecture at the Pittsburgh
Links Among Analysis and Number Theory conference at Carnegie
Melon University

Title: TBA

January 29-February 2, 2024 An invited plenary lecture at the
Renyi Institute conference on Fourier Analysis and Additive
Problems

Title: Uniform distribution and pseudo-randomness

**2023 **(382)

December 8-10, 2023, Analysis Conference at
Georgia Tech

Title: Exact signal recovery and restriction theory

November 2023, Number Theory Seminar, Istanbul

Title: Exact
signal recovery and restriction theory

October 6, 2023 HSA Conference

Title: Exact signal recovery
and restriction theory

September 22-24, 2023, International Conference on Approximation
and Potential Theory, Savannah, GA

Title: Exact signal recovery and restriction theory

September 15, 2023 University of Rochester Analysis Seminar

Title: Exact
signal recovery and restriction theory

August 2023 An invited series of lectures at the Informal
Analysis Seminar at Kent State University (four lectures)

Title: Geometric measure theory and data science

July 17-19, 2023 An invited plenary lecture at the Vietnam
National University Geometry Conference

Title: Finite point configurations: challenges and
opportunities

July 2023 An invited lecture series at the University of Harbin,
China (6 lectures)

Title: Geometric measure theory and applications

July 2023 An invited lecture at the University of Tbilisi,
Georgia

Title: Finite point configurations and complexity

July 2023 An invited lecture at the
Mathematics in Armenia: Advances and Perspectives conference
in Yerevan, Armenia

Title: Finite point configurations: analytic,
combinatorial, and number theoretic features

June 29, 2023 An invited lecture at the Number Theory Web
Seminar

Title: Applications of lattice point bounds to data
science

June 2023 An
invited talk the Harmonic analysis, partial differential
qquations and geometric measure theory in Bilbao 2023
conference

Title: Learning theory, complexity and point
configurations

June 4-9, 2023 A research
visit to Oberwalfach (MFO) program Incidence problems in
Harmonic analysis, geometric measure theory and ergodic theory

May 2023 An invited talk at the annual meeting of the Italian
harmonic analysts in Milan, Italy

Title: Times series, complexity and learning theory

May 2023, An invited talk at Combinatorics and Number Theory
Conference at CUNY

Title: A variant of the Erdos distance problem in vector
spaces over finite fields

May 19, 2023 An invited analysis seminar talk at Concordia
University, Montreal, Canada

Title: Simplexes in Euclidean space and the
Vapnik-Chervonenkis dimension

April 26, 2023 An
invited Pi Mu Epsilon Lecture at the University of
Nebraska-Lincoln

Title: From analysis to combinatarics to number theory and
back

April 26, 2023 An invited Discrete Mathematics seminar at the
University of Nebraska-Lincoln

Title: Vapnik-Chervonenkis dimension and point
configurations in vector spaces over finite fields

April 15-16, 2023 An invited talk at the AMS Sectional Meeting
in Cincinnati- Special Session on the interface of geometric
measure theory and harmonic analysis

Title: Uniform distribution, point configurations and
pseudo-randomness

March 25-26, 2023 An invited plenary talk at Harmonic
Analysis and Fractal Sets Conference at the Ohio State
University

Title: Fractal analysis and complexity theory

March 18-19, 2023 An invited talk at the AMS Spring Southeastern
Sectional Meeting in Atlanta, GA

Title: Vapnik-Chervonenkis dimension, systems of equations
and point configurations

March 17, 2023 An invited analysis seminar talk at Clemson
University

Title: VC-dimension and the Falconer distance problem

March 7, 2023 An invited colloquium talk at the University of
Alabama

Title: Point configurations and complexity theory

March 1, 2023 An invited seminar talk at Brown University

Title: Complexity and finite point configurations

February 2023 An invited talk at the Institute for Advanced
Study (Princeton)

Title: Finite point configuration and the
Vapnik-Chervonenkis dimension

Feburary 2023 An invited talk at the CUNY combinatorics seminar

Title: Graphs, multi-linear forms and operators

February 2023 An invited seminar talk at the Institute for
Advanced Study, Princeton

Title: Complexity and finite point configurations

January 2023 An invited talk at the NYU/CUNY Geometry Seminar

Title: Complexity and point configurations

January 2023 An invited lecture at the JMM Special Session on
Distance problems in continuous, discrete and finite field
settings

Title: Distance problems and the VC-dimension

**2022 **(346)

December 2022 An invited talk at the CMS
Special Session on Approximation Theory

Title: Vapnik-Chervonenkis dimension and point
configurations

November 2022 An invited talk at the Extremal Problems in
Harmonic Analysis, Convexity and Bellman functions ICERM
conference

Title: Discrete energy and large data sets

November 2022 An invited talk at the Banff meeting on analytic
and probabilistic combinatorics

Title: Vapnik-Chervonenkis dimension and Erdos type
problems

November 2022 An invited colloquium talk at the Northern
Illinois University

Title: Finite point configurations: analysis, arithmetic
and complexity

November 2022 An invited talk at the Workshop on Harmonic
Analysis (Beijing)

Title: Finite point configurations and frames

November 2022 An invited talk at the analysis seminar at the
University of Pennsylvania

Title: Geometric measure theory and machine learning

October 2022 An invited talk at the Discrete Analysis Working
Group Part 4

Title: Group actions and finite point configurations

October 2022 An invited talk at the Discrete Analysis Working
Group Part 3

Title: The Erdos-Falconer distance problem over finite
fields

October 2022 An invited colloquium lecture at IUPUI

Title: Complexity and finite point configurations

October 2022 An invited seminar lecture at the IUPUI graduate
student seminar

Title: Tiling and bases in vector spaces over finite
fields

October 2022 An invited talk at the Discrete Analysis Working
Group Part 2

Title: Fuglede conjecture in the plane over the integer
modulo a prime

October 2022 An invited lecture at the University of Toronto
analysis seminar

Title: On some connections between geometric measure
theory and data science

October 2022 An invited at the Discrete Analysis Working Group
Part 1

Title: Sums, products and finite point configurations

September 2022 An invited lecture at the University of Rochester
number theory seminar

Title: Vapnik-Chervonenkis dimension and finite point
configurations

September 2022 An invited lecture at SUMS (University of
Rochester undergraduate mathematics club)

Title: Several proofs of the infinity of primes, and a few
comments on why undergraduate research is essential

August 2022 An invited lecture at the University of Hanoi

Title: Uniform distribution and point configurations

August 2022 A presentation to perspective students at the branch
office of the University of Rochester in Ho Chi Minh City

Title: Why Rochester is a great place for foreign students

June 2022 An invited lecture at the University of the Basque
Country

Title: From geometric measure theory to data science

June 2022 An invited lecture at CRM Barcelona in honor of
Michael Lacey's 60th birthday

Title: From
geometric measure theory to data science

June 2022 An invited lecture at the Harmonic Special Session at
the CMS conferene in St Johns, Newfoundland, Canada

Title: Point configurations and exponential frames

May 2022 An invited lecture at Combinatorics Meeting at JKH,
Linz, Austria

Title: Point configurations and the Vapnik-Chervonenkis
dimension

May 2022 An online lecture at the Currents Trends in Abstract
and Applied Analysis conference in Ivano-Frankivsk

Title: Exponential bases, point configurations and
curvature

April 2022 An invited talk at the analysis seminar at UCLA

Title: Some general perspectives on point configurations
in Euclidean space

March 2022 An invited colloquium talk at the University of
Arizona

Title: Fourier series and point configurations

March 2022 An invited lecture at the University of Rochester
SUMS

Title: Cauchy-Schwartz and friends

February 2022 An invited talk at the Korea-Taiwan-Vietnam Joint
Seminar

Title: A universal viewpoint on finite point
configurations

February 2022 An invited talk at the University of Arizona
Dynamical Systems Seminar

Title: Finite point configurations

January 2022 An invited colloquium talk at the University of
Vermont

Title: Analytic, number-theoretic, and combinatorial
aspects of finite point configurations, and applications to data
science

**2021 **(318)

October 2021 A presentation to the Ohio State
mathematics undergraduates about how to apply and prepare for
graduate programs in mathematics

Title: Graduate school and beyond

October 2021 An invited lecture at Seminari a Distanze di
Analisis Armonica

Title: The Vapnik-Chervonenkis dimension and point
configurations

September 2021 An invited number theory seminar lecture at
Williams College

Title: The Vapnik-Chervonenkis dimension and point
configurations

August 2021 An invited
lecture at the International Seminar Series on Harmonic
Analysis and Applications

Title: Point configurations, operator bounds and
complexity

June 2021 An invited Lecture at the
Harmonic and Spectral Analysis Conference

Title: On graphs, group actions and point sets

May 2021 An invited lecture at the Combinatorics and Number
Theory Confierence

Title: On graphs, group actions and point sets

May 2021 An invited lecture at the online AMS conference

Title: On point configurations and frame theory

February 2021 An invited lecture at the Point Distributions
Webinar

Title: On point configurations and frame theory

2020

November 2020 An invited lecture at CUNY Number Theory seminar

Title: Discrete energy and applications to combinatorial geometry

October 2020 An invited lecture at the FFT seminar (Norbert Wiener Center)

Title: Exponential frames and curvature

June 2020 An invited lecture at the CodEx2020 seminar

Title: Finite point configurations and frame theory

June 2020 An invited lecture at Mel Nathanson 75th birthday conference at CUNY (zoom)

Title: An approximate version of Erdos' single distance conjecture

June 2020 An invited lecture at the annual meeting of Italian harmonic analysts (zoom)

Title: A survey of recent results on distance sets and point configurations

February 2020 An invited colloquium lecture at the Florida International University

Title: Configuration problems and frame theory

February 2020 An invited seminar talk at the Florida International University

Title: Sums and products in integers modulo a prime

January 2020 JMM Special Session on Geometric Combinatorics

Title: Triangles, quadrilaterals and group actions

**2019 **(302)

December 2019 An invited lecture in
Hanoi, Vietnam

Title: Discrete and analytic aspects of incidence theory

September 2019 An invited lecture at the University of Missouri
analysis conference

Title: Curvature and frame theory

June 2019 An invited lecture at the Harmonic Analysis and PDE
conference in Helsinki, Finland

Title: On configuration problems and applications in
classical analysis and beyond

June 2019 An invited lecture at the harmonic analysis in
Tianjin, China

Title: On configuration problems and applications in
classical analysis and beyond

May 2019 A keynote lecture at the conference in Holon, Israel in
honor of Vladimir Mazya's 80th birthday

Title: On orthogonal Gabor bases in the presence of
curvature

May 2019 A special analysis seminar at Cornell

Title: Analytic and combinatorial methods in frame theory

April 2019 Colloquium at the University of Miami

Title: Analytic, geometric and combinatorial aspects of
finite point configurations

March 2019 A lecture at the LeMoyne University Math Club

Title: The Erdos distance problem

March 2019 An analysis seminar lecture at the University of
Pennsylvania

Title: On the continual symbiosis between frame theory and
geometric combinatorics

March 2019 An analysis seminar lecture at the University of
Illinois

Title: Some recent developments on the Erdos and Falconer
distance problems and applicationsiet

February 2019 A plenary lecture at the Weitzmann Institute
Conference in honor of Alexander Olevskii

Title: Geometric measure theory and applications to frame
theory

January 2019 A plenary lecture at the Second Vietnam Workshop on
Graph Theory and Discrete Geometry, Hanoi, Vietnam

Title: Erdos distance problem for smooth metrics

**2018 **(290)

November 2018 A plenary lecture at the Mid
Atlantic Analysis Meeting, Virgina Tech University

Title: Finite point configurations: from Furstenberg to
Falconer

October 2018 A plenary lecture at the NEAM2018 analysis
conference

Title: Gabor bases and geometric measure theory

September 2018 An invited lecture at the Fourier Bases
conference in Iraklion, Greece

Title: Gabor bases and the Erdos distance problem

September 2018 A plenary lecture at the 7th International
Conference "Harmonic Analysis and Approximation", Armenia

Title: Finite point configurations and frame theory

August 2018 Faculty colloquium at Penn State University

Title: Finite point configurations

August 2018 MASS colloquium at Penn State University

Title: Tiling and exponential bases: analytic,
combinatorial and number theoretic ideas

August 2018 Number theory seminar at Penn State University

Title: Some number theoretic aspects of the theory of
exponential bases

June 2018 An invited lecture at the ICERM workhop Frame Theory
and Exponential Bases

Title: On interaction between geometric measure theory and
the existence problems for exponential bases

May 2018 An invited lecture at the Workshop on Real Analysis and
its applications to partial differential equations and geometric
measure theory, in honor of Steve Hofmann's 60th birthday,
ICMAT, Madrid

Title: Analytic and combinatorial aspects of frame theory

May 2018 American Engagement Network conference in Washington
D.C.

May 2018 An invited lecture at the CalTech Analysis Seminar

Title: Gabor bases and geometric combinatorics

March 2018 An invited lecture at the University of
Massachusetts-Lowell

Title: Finite point configurations: congruence and
rigidity

March 2018 An invited lecture at the University of Tel-Aviv
analysis seminar

Title: Exponential bases and Gabor bases: discrete and
continuous aspects

February 2018 A research visit to ICERM

February 2018 An invited lecture series at the Louisiana State
University

Title: The Falconer conjecture and connections with frame
theory

February 2018 An invited colloquium talk at the Arizona State
University

Title: Combinatorial, number theoretic and analytic
aspects of frame theory

February 2018 An invited number theory seminar lecture at the
Arizona State University

Title: The Fuglede Conjecture in vector spaces over prime
fileds

January 2018 An invited lecture series (two lectures) at the
Vietnam University of Science

Title: Geometric combinatorics in vector spaces over
finite fields

January 2018 An invited lecture at the Vietnam Institute of
Mathematics

Title: The Fuglede conjecture in vector spaces over finite
fields

**2017 **(272)

December 2017 A colloquium lecture at the
University of Massachusetts-Lowell

Title: On discrete and continuous aspects of frame theory

October 2017 An invited seminar lecture at the Georgia Institute
of Technology analysis seminar

Title: Indicator functions of smooth convex sets cannot
serve as window functions for orthogonal Gabor bases

October 2017 An invited lecture at the Oberwolfach meeting on
Geometric Measure Theory

Title: Lp-dimension and application to the Furstenberg
intersection conjecture

September 2017 An invited 40 minute lecture at the AMS Session
on Global Analysis at the University of Central Florida

Title: Finite point configurations

September 2017 An invited lecture at the conference in honor of
Eli Stein in Wroclaw, Poland

Title: Finite point configurations: analysis,
combinatorics and number theory

August 2017 A plenary lecture at the CIMPA 2017 Buenos Aires,
Argentina

Title: Finite point configurations: analysis,
combinatorics and number theory

May 2017 An invited lecture at the conference in honor of Peter
Jones in Seoul, Korea

Title: Rigidity, simplexes and multi-linear operators

May 2017 An invited lecture at the MSRI workshop on harmonic
analysis

Title: Rigidity, simplexes and multi-linear operators

April 2017 An AMS Special Session on Frame Theory at Hunter
College, NYC

Title: Finite point configuration and the underlying
operators

March 2017 A colloquium talk at Virginia Tech University

Title: Analytic, number theoretic and combinatorial
perspectives on orthogonal bases and tiling

March 2017 A plenary lecture at the Ohio River Analysis Meeting

Title: On bi-linear analogs of generalized Radon transform

January 2017 An invited lecture at the JMM2017 Special Session
for women in mathematics dedicated to Cora Sadosky

Title: A group action approach to the non-trivial exponent
for every point configuration in vector spaces over finite
fields

** 2016 **(260)

Title: Fourier bases and tiling

November 2016 An invited lecture at the University of Delaware Analysis Seminar

Title: The Fuglede conjecture in vector spaces over finite fields

October 2016 A colloquium talk at SUNY Albany

Title: Finite point configurations in discrete, continuous and arithmetic settings

October 2016 A plenary lecture at the Northeast Analysis Meeting

Title: The Fuglede conjecture holds in vector spaces over finite fields

October 2016 A plenary lecture at the Integers conference in Georgia.

Title: The analysis, combinatorics and number theory of the distance graph

September 2016 An invited lecture at the Prairie Analysis Seminar 2016

Title: Distribution of simplexes in fractal subsets of Euclidean space

September 2016 A keynote address at the combinatorial geometry conference in Hanoi, Vietnam

Title: The analysis, combinatorics and number theory of the distance graph

September 2016 A colloquium talk at Ohio State University

Title: The analysis, combinatorics and number theory of finite point configurations

June 2016 An invited lecture at the CRM analysis conference, Barcelona, Catalonia.

Title: The analysis, combinatorics and number theory of the distance graph

June 2016 An invited lecture at the conference on discrepancy theory in Varenna, Italy.

Title: The analysis, combinatorics and number theory of the distance graph

May 2016 An invited lecture at the CANT 2016 conference at CUNY

Title: The analysis, combinatorics and number theory of the distance graph

April 2016 An invited lecture at the Syracuse analysis seminar

Title: Fuglede conjecture holds in two dimensional vector spaces over finite fields

February 2016 An invited lecture at ICERM workshop on Geometric Measure Theory

Title: Finite point configurations in Euclidean space

Feburary 2016 A colloquium lecture at George Washington University

Title: The Fuglede Conjecture: analysis, combinatorics and number theory

February 2016 An invited lecture at FFT 2016, University of Maryland

Title: Geometric configurations and Fourier analysis

**2015 **(245)

December 2015 An invited lecture at the joint
CUNY/NYU Analysis seminar

Title: The Fuglede conjecture in vector spaces over finite
fields

December 2015 An invited lecture at the Ohio State Analysis/PDE
seminar

Title: The Fuglede conjecture in vector spaces over finite
fields

Setember 2015 An invited lecture at the CIRM Number Theory
conference in Marseilles, France

Title: The Fuglede conjectre holds in two-dimensional
vector spaces over finite fields

May 2015 An invited lecture at CANT 2015 conference at the CUNY
Graduate Center

Title: The Fuglede Conjecture holds in two dimensional
vector spaces over prime fields.

May 2015 A plenary lecture at the Complex Analysis and Dynamical
Systems VII conference in Nehariya, Israel

Title: The Fuglede Conjecture holds in two dimensional
vector spaces over prime fields.

April 2015 An invited colloquium lecture at Worcester
Polytechnic Institute

Title: Some simple ideas in the study of simplexes in
Euclidean space

March 2015 An invited at the sectional AMS meeting in Washington
D.C.

Title: Density of exponential frames and spectra in
fractal domains

February 2015 An invited colloquium lecture at the University of
Massachusetts-Lowell

Title: Distribution of simplexes, geometric combinatorics
and fractals

**2014 **(237)

Title: Distribution of simplexes in fractal subsets of the Euclidean space and Riemannian manifolds

December 2014 An invited lecture at the CMMSC One Day Workshop at NCTU, Taiwan

Title: Convolution operators on fractal domains and applications to geometric measure theory

July 2014 An invited lecture at the Oberwalfach Harmonic Analysis meeting

Title: Fractal analogs of classical Fourier inequalities

April 2014 An invted lecture at the IPAM workshop II

Title: Geometric configurations in vector spaces over finite fields

April 2014 An invited lecture at sectional meeting of the AMS in Baltimore

Title: Trace inequalities and application to multi-linear bounds

March 2014 An invited lecture at the IPAM workshop I

Title: The square root law and the structure of rings

March 2014 An invited lecture at IPAM graduate student tutorials

Title: Erdos type problems in discrete, continuous and arithmetic settings

January 2014 An invited lecture at joint meetings of the AMS

Title: Distribution of simplexes in arithmetic settings

January 2014 An invited lecture at the geometry seminar at Tel-Aviv University

Title: Distribution of simplexes in arithmetic settings

January 2014 An invited lecture at the analysis seminar at Bar-Ilan University

Title: An elementary viewpoint on multi-linear operators

**2013** (227)

December 2013 An invited seminar lecture at
the University College London

Title: An elementary viewpoint on multi-linear operators

December 2013 An invited seminar lecture at the Reading
University

Title: Distribution of simplexes in arithmetic settings

December 2013 An invited lecture at the Heilbron Seminar,
University of Bristol

TItle: Distribution of simplexes in arithmetic settings

September 2013 A colloquium lecture at Kent State University

Title: Restricted convolution inequalities, multilinear
operators and applications

September 2013 An invited lecture at the Kent State Analysis
Seminar

Title: Some elementary observations about multi-linear
operators

August 2013 An invited lecture at the Kent State Analysis
Seminar

Title: Group actions and distribution of simplexes in the
Euclidean space

May 2013 An invited lecture at the Integral Transforms and
Spectral Theory in Analysis and Geometry workshop in Nahariya,
Israel

Title: Intersections of sets, group actions and
Erdos-Falconer problems

April 2013 An invited lecture at the University of Minnesota
PDE-Analysis seminar

Title: Trace inequalities, multi-linear operators and
geometric applications

March 2013 University of Rochester Number Theory Seminar

Title: From fractals to diophantine equations

March 2013 An invited lecture at the Analysis Symposium at the
University of Georgia

Title: Intersections of sets and Fourier Analysis

February 2013 A colloquium lecture at the University of Georgia

Title: Simplexes and Fourier Analsysis

**2012** (216)

Title: Multi-linear operators, geometric measure theory and combinatorics

October 2012, University of Rochester Number Theory Seminar

Title: Beck's theorem and areas of triangles in planes over finite fields

October 2012 AMS Sectional Meeting in Akron, OH, special session on harmonic analysis and convex geometry

Title: Trace inequalities, multi-linear operators and applications

October 2012 An invited colloquium lecture at the University of Southern Georgia

Title: Analytic methods in geometric combinatorics

September 2012 AMS Sectional Meeting in Rochester, NY, Special Session on Number Theory

Title: Distribution of lattice points in annuli and geometric measure theory

September 2012 AMS Sectional Meeting in Rochester, NY, Special Session on Partial Differential Equations

Title: Bilinear estimates and applications

August 2012 Lecture series at Chungbuk University, South Korea

Title: Convolution inequalities, multi-linear operators and geometric measure theory

May 2012 A series of lectures at the CANT2012 conference in CUNY, New York City

Title: Harmonic analysis in geometric combinatorics

April 2012 An invited expository lecture for graduate students at the Probabilistic Methods in Harmonic Analysis conference in Bedlewo, Poland

Title: From analysis to combinatorics

April 2012 An invited lectre at the Probabilistic Methods in Harmonic Analysis conference in Bedlewo, Poland

Title: Multi-linear generalized Radon transforms and applications to geometry and combinatorics

April 2012 A colloquium talk at SUNY-Albany

Title: Bilinear operators and geometric combinatorics

April 2012 An invited lecture at the special session on harmonic analysis at the AMS sectional meeting in Lawrence, KS

Title: Lattice points, multi-linear operators and distribution of simplexes

March 2012 An invited lecture at the analysis seminar at the Univeristy of Pennsylvania

Title: Multi-linear operators, geometric measure theory and discrete geometry

March 2012 An invited lecture at the applied mathematics seminar at the University of Delaware

Title: Applications of multi-linear operator bounds to problems in geometry

March 2012 An invited lecture at the discrete mathematics seminar at the University of Delaware

Title: Distribution of simplexes in vector spaces over finite fields

March 2012 An invited lecture at the analysis seminar at Princeton University

Title: Distribution of simplexes in discrete and continuous settings and multi-linear operators

March 2012 A presentation to the graduate students at Paris-Orsay

Title: The method of stationary phase, elementary incidence theory and connections beween the two

March 2012 An invited lecture at the analysis seminar at the University of Paris-Orsay

Title: Multi-linear operators and geometric measure theory

January 2012 An invited lecture at AMS special session in Boston

Title: Finite point configurations in Euclidean space

January 2012 An invited lecture at the Tufts workshop on Geometric and Fourier analysis

Title: Multi-linear generalized Radon transforms and applications to geometric measure theory

**2011** (196)

October 2011 An invited lecture at the MIT
analysis seminar

Title: Generalized Radon transforms, lattice points near
families of surfaces and non-isotropic dilations

September 2011 AMS conference at
Ithaca, NY

Title: Regular value theorem in a fractal setting

July 2011 An invited lecture at the Fields Institute conference
in honor of Eric Sawyer (was unable to cross the border due to a
paperwork mixup)

Title: Lattice points, fractal sets and generalized Radon
transforms

June 2011 An invited lecture at the Edinburgh Workshop on
Harmonic Analysis

Title: Geometric consequences of analytic inequalities

June 2011 An invited lecture at the analysis/combinatorics
seminar at the University of Bristol

Title: The paraboloid: a ubiquitous counter-example

June 2011 An invited lecture at the University of Cardiff

Title: Application of generalized Radon transforms to
problems in geometric measure theory

May 2011 An invited lecture at CANT conference at CUNY

Title: On directions determined by subsets of vector
spaces over finite fields

May 2011 An invited lecture at the Banff meeting on convex
geometry

Title: Distribution of lattice points near families of
surfaces

April 2011 An invited lecture at the University of South
Carolina workshop on harmonic analysis

Title: Lattice points, fractal sets and generalized Radon
transforms

April 2011 A faculty colloquium talk at the University of
Rochester

Title: Discrete and continuous aspects of incidence
theory

April 2011 An invited lecture at the Informal Analysis Seminar
at Kent State University

Title: Harmonic analytic estimates in geometric measure
theory

March 2011 Analysis seminar at the Kennesaw State University

Title: Fourier analytic methods in sum-product theory

March 2011 Colloquium at the Clayton State University

Title: On sums and products in finite fields

March 2011 AMS conference at Statesboro, GA

Title: Distribution of lattice points near variable
families of surfaces in Euclidean space

March 2011 AMS conference at Statesboro, GA

Title: Regular value theorem in a fractal setting

February 2011 Analysis seminar at the University of Miami

Title: Regular value theorem in a fractal setting and
connections with discrete geometry and number theory.

February 2011 Anaysis seminar at the Florida International
University

Title: Regular value theorem in a fractal setting and
connections with discrete geometry and number theory.

January 2011 Joint meeting of the analysis and combinatorics
seminars at the University of Pennsylvania

Title: Regular value theorem in a fractal setting and
connections with discrete geometry and number theory.

January 2011 Colloquium, Pennsylvania State University

Title: Regular value theorem in a fractal setting.

January 2011 AMS Special Session on Integral Geometry at the
Annual Meeting of the AMS in New Orleans

Title: Finite point configurations in the continuous
setting.

January 2011 LSU workshop on geometry and analysis

Title: Regular value theorem in a fractal setting.

**2010** (175)

December 2010 Special session on spectral
theory at the CBMS conference in Vancouver, Canada

Title: On a fractal variant of the regular value theorem

December 2010 Special session on harmonic analysis and additive
number theory at the CBMS conference in Vancouver, Canada

Title: On simplexes determined by subsets of the
Euclidean space.

November 2010 Graduate student seminar at CUNY

Title: On a fractal variant of the regular value theorem

October 2010 Number theory seminar at the University of
Rochester

Title: Sums and products in discrete and continuous
settings

October 2010 An analysis seminar at the University of British
Columbia

Title: On sums-product theorem and simplexes in vector
spaces over finite fields

September 2010 An analysis seminar lecture at Cornell University

Title: On simplexes determined by fractal subsets of the
Euclidean space

March 2010 An invited lecture at Centro di Ricerca Matematica
Enrico di Giorgi, Pisa

Title: Finite point configurations in discrete and
continuous settings

January 2010 An analysis seminar talk at the Michigan State
University

Title: Uniform distribution, finite point configurations
and number theoretic consequences

**
2009** (168)

December 2009 An invited 40 minute lecture at
the AMS/Korean Mathematical Society Special Session on Harmonic
Analysis in Seoul, Korea

Title: Finite point configuration in the Euclidean
setting via Fourier analysis and geometric combinatorics

November 2009 An invited lecture at the AMS Special Session on
Addition Number Theorey at the University of
California-Riverside

Title: Uniform distribution, pseudo-random graphs and
finite point configurations in Euclidean space

July 2009 An invited lecture at the University of Crete

Title: Finite point configurations in discrete and
continous settings

June 2009 An invited lecture at the University of Milano

Title: Finite point configurations in discrete and
continous settings

June 2009 An invited lecture at the Conference on Harmonic
Analysis, Geometric Measure Theory and Quasiconformal Mappings
at CRM, Barcelona

Title: Finite point configurations in discrete and
continous settings

May 2009 An analysis seminar lecture at the University of
Arizona

Title: Finite point configurations in discrete and
continous settings

April 2009 An invited lecture at the Spring Lecture Series 2009,
University of Arkansas

Title: Geometric configurations in Euclidean space the
associated models in vector spaces over finite fields

February 2009, A colloquium talk at the University of
Illinois-Chicago

Title: Sums and products in discrete, continuous and
arithmetic settings

February 2009, A seminar talk at the University of Illinois at
Urbana-Champaign

Title: Geometric configurations in the discrete and
continuous settings

January 2009, A colloquium talk at Rochester University

Title: Geometric configurations in discrete, continuous
and number theoretic settings

**2008** (158)

November 2008, An invited seminar lecture at
the University of Wisconsin-Madison

Title: Geometric configurations in fractals

October 2008, An analysis seminar talk at the Arizona State
University

Title: Geometric configurations in fractals

October 2008, A colloquium talk at the Arizona State University

Title: Geometric configurations in Euclidean, integer and
finite field geometries: combinatorial and algebraic aspects

October 2008, A series of lectures at Baylor University

Title: Geometric combinatorics, arithmetic and Fourier
analysis

September 2008, An invited lecture at Oberwolfach (Discrete
Geometry)

Title: Geometric configurations in Euclidean, integer and
finite field geometries: combinatorial and algebraic aspects

July 2008, An invited lecture at the
University of Crete

Title: Mixed norm restriction theorems and connections
with fractal geometry

July 2008, An invited lecture at the University of Padova

Title: Geometric configurations in Euclidean, integer and
finite field geometries

July 2008, An invited lecture at the University of Torino

Title: Geometric configurations in Euclidean, integer and
finite field geometries

July 2008, An invited lecture at Oberwolfach (Harmonic Analysis)

Title: Geometric configurations in Euclidean, integer and
finite field geometries

June 2008, An invited lecture at the Arizona State University
MTBI program

Title: Geometric configurations: an elementary
viewpoint

April 2008, A seminar lecture at Wayne State University

Title: Fourier analysis in vector spaces over finite
fields

April 2008, An invited lecture at the Fields Institute
Conference on Additive Number Theory

Title: Distribution of dot products in vector spaces in
finite fields and applications to problems in additive number
theory and geometric combinatorics

March 2008, A colloquium talk at the McMaster University

Title: Harmonic analysis in vector spaces over finite
fields and applications to additive combinatorics

**2007 **(145)

October 2007, A seminar talk at the Louisiana
State University

Title: Radon transforms and applications to problems in
additive number theory

October 2007, A colloquium at the
Louisiana State University

Title: Incidence theory: discrete, continous and
arithmetic aspects

October 2007, An invited 50 minute
address to the American Mathematical Society at DePaul
University, Chicago

Title: Incidence theory: discrete, continous and
arithmetic aspects

October 2007, A colloquium talk at the University of Indiana,
Bloomington

Title: Sums and products in finite fields- an analytic
perspective

September 2007, An invited lecture at the agebra seminar at
Emory

Title: Sums and products in finite fields

September 2007, An invited lecture at the analysis seminar at
Georgia Tech

Title: Radon transforms and applications to problems in
additive number theory

September 2007, An invited lecture at a mini-conference on
discrepancy theory at the University of South Carolina

Title: Radon transforms and applications to problems in
additive number theory

September 2007, A colloquium lecture at the University of
Cincinnati

Title: Radon transforms and applications to problems in
additive number theory

September 2007, A seminar talk at the Georgia Institute of
Technology

Title: Sums and products in finite fields- an analytic
perspective

August 2007, A seminar talk at UMKC (Kansas City)

Title: Sums and products

June 2007, An invited lecture at the University of Padova

Title: Integral geometric viewpoint on sums and products
in finite fields

June 2007, An invited lecture at the University of Bologna

Title: Incidence theory via Fourier analysis in vector
spaces over finite fields

June 2007, An invited lecture at the University of Milan

Title: Integral geometric viewpoint on sums and products
in finite fields

May 2007, An invited lecture at the annual meeting of Italian
harmonic analysts at Caramanico

Title: Incidence theory via Fourier analysis and
applications to geometry and arithmetic

May 2007, A seminar lecture at the University of Bergamo

Title: Integral geometric viewpoint on sums and products
in finite fields

April 2007, DePaul University analysis seminar

Title: Fourier analysis and incidence theory

March 2007, A colloquium lecture at the Bogazici University

Title: Analytic, combinatorial and number theoretic
aspects of incidence theory

March 2007, A lecture at the Istanbul Institute of Mathematics

Title: Sums/Products via Fourier analysis

March 2007, King's College, London, an analysis seminar lecture

Title: Ramsey Theory and Fourier analysis

March 2007, An invited 50 minute
address to the American Mathematical Society at Davidson
College, North Carolina

Title: Incidence theory: discrete, continous and
arithmetic aspects

January 2007, An invited lecture at Bar-Ilan University

Title: Geometric combinatorics via Fourier analysis

**2006 **(124)

November 2006, A seminar talk at the
University of Crete

Title: Sums and products in finite fields via Kloosterman
sum estimates.

October 2006, AMS lecture in Salt Lake
City, Utah

Title: Sums and products in finite fields via
Kloosterman sum estimates.

September 2006, A seminar lecture at Michigan State University

Title: Erdos/Falconer distance problem in vector
spaces over finite fields.

August 2006, An invited lecture at the Rudelson CBMS lecture
series conference at Kent State University

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, An invited lecture at the Koldobsky CBMS lecture
series conference at the Kansas State University

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, A lecture at the Universidad Autonoma Barcelona (CRM)

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, A lecture at the University of Milano

Title: Analysis, combinatorics and number
theory of the Mattila integral-lattice points on surfaces.

July 2006, A lecture at the University of Bergamo

Title: Analysis, combinatorics and number
theory of the Mattila integral-Fourier analysis in finite
fields.

June 2006, a plenary lecture at Harmonic Analysis conference in
Zharos, Crete

Title: Analysis, combinatorics and number
theory of the Mattila integral.

April 2006, AMS Special Session in Miami

Title: Erdos/Falconer distance problem in
vector spaces over finite fields

March 2006, Combinatoria Number Theory program in Montreal

Title: Fourier analytic approach to incidence
theorems in vector spaces over finite fields

January 2006, Colloquium at Northeastern University

Title: Analytic, combinatorial and number
theoretic aspects of distance set theory

January 2006, Colloquium at the University of Georgia

Title: Analytic, combinatorial and number
theoretic aspects of distance set theory

January 2006, Analysis Seminar, University of Crete

Title: Erdos/Falconer distance problems in
vector spaces over finite fields

January 2006, Pure Mathematics Seminar, University of Bristol

Title: Erdos/Falconer distance problem in
vector spaces over finite fields

**2005 **(109)

Title: Erdos distance problem in vector spaces over finite fields

November 2005 Colloquium lecture at Kent State University

Title: Analytic, combinatorial and number theoretic aspects of distance set theory

October 2005, lecture at the Integers conference at the University of Western Georgia

Title: Erdos distance problem in vector spaces over finite fields

October 2005, seminar talk at the University of South Carolina

July 2005 University of Crete, Greece

Title: Mean square averages of the Fourier transform and geometric combinatorics

July 2005, Oberwalfach, Germany

Title: Some observations on the interaction of harmonic analysis and geometric combinatorics

June 2005, University of Orleans, France

Title: Mean square averages of the Fourier transform and geometric combinatorics

June 2005, University of Bristol, England

May 2005, CUNY conference in honor of Mel Nathanson's 60th birthday

Title: Analysis and combinatorics of distance sets

January 2005, Texas A&M University

Title: Gaussian curvature, geometric combinatorics, and the Fourier transform

**2004 **(101)

September 2004 AIM workshop on additive number
theory/ geometric combinatorics

July 2004 Trimester in Harmonic
Analysis, Pisa, Italy

Title: Average decay of the Fourier transform and
applications

June 2004 University of Madrid, Spain,
Analysis Seminar

Title: Combinatorial complexity of convex
sequences and related problems in combinatorial geometry

June 2004 Trimester in Harmonic Analysis, Pisa, Italy

Title: Combinatorial complexity of convex
sequences and connections with Fourier analysis

May 2004 Georgia Institute of
Technology; an invited lecture associated with

a series of CBMS lectures to be
delivered by C. Thiele.

Title: Combinatorial complexity of convex
sequences

May 2004 CUNY Conference on Additive
and Combinatorial Number Theory

Title: Combinatorial complexity of convex
sequences

May 2004 University of Edinburgh

Title: Some remarks on the Mattila integral and
related problems

May 2004, University of Bristol,
England

Title: Mean square discrepancy bounds for the
distribution of lattice points in convex domains

April 2004, University of Athens

Title: Convex sequences and the Erdos/Falconer
distance problems

April 2004, University of Crete

Title: Some remarks on the Mattila integral

March 2004 Annual meeting of the
Italian harmonic analysts (plenary lecture)

Title: Some remarks on the Mattila integral

March 2004 University of Bergamo,
Italy, seminar

Title: Average decay of Fourier transforms of
measures and applications

March 2004 University of Milano,
Italy, seminar

Title: Combinatorial complexity of convex
sequences and related problems

March 2004 Florida State University,
AMS Special Session on Harmonic Analysis

Title: Combinatorial complexity of convex
sequences

February 2004 University of Michigan
(differential equations seminar)

Title: Average decay of the Fourier
transform, Salem sets, and related problems

January 2004, Temple University,
Philadelphia (colloquium)

Title: Combinatorial complexity of convex
sequences: combinatorial and analytic methods

**2003 **(86)

December 2003, University of British
Columbia (research collaboration with I. Laba)

November 2003, University of
California-Los Angeles

Title: Distribution of lattice points in convex
domains: mean square estimates

October 2003, Conference on additive
number theory, University of West Georgia

Title: Distribution of lattice points in convex
domains: mean square estimates

October 2003, University of
Wisconsin-Madison

Title: A Weyl type formula for exponential spectra
and frames

June 2003, Harmonic Analysis and
Partial DIfferential Equations; Annual Summer Session

Title: Combinatorial approach to orthogonal
exponentials

June 2003, Joint meeting of the Real
Sociedad Mathematika Espanola and the AMS in Seville, Spain

Title: Variants of the Falconer and Erdos distance
problems

June 2003, University of Milan

Title: Variants of the Falconer and Erdos
distance problems

May 2003, Conference on additive
number theory and applications to harmonic analysis

Title: Applications of geometric measure and
geometric combinatorics in harmonic analysis

May 2003, Princeton University
Analysis Seminar

Title: Combinatorics of distance sets and
applications

April 2003, Riviere-Fabes Symposium in
Analysis

Title: Analysis and combinatorics of distance set

March 2003, The Erwin Schrodinger
International Institute for Mathematical Physics

Title: Analysis and combinatorics of distances sets

February 2003, Georgia Institute of
Techology (research collaboration)

**2002 **(76)

October 2002, AMS Special Session in Madison,
Wisconsin

Title: "Distribution of lattice points inside
random ellipsoids"

July 2002, Convex geometry workshop in
Vancouver, Canada

Title: "Lattice points inside random
ellipses"

June 2002, University of Milano, Bicocca

Title: "Distribution of lattice points inside
random ellipses"

June 2002, University of Pisa, AMS
Special Session

Title: "Convex bodies, orthogonal exponentials and
geometric combinatorics"

June 2002, Universidad Autonoma de
Madrid

Title: "Some elementary combinatorial geometry and
applications to harmonic analysis"

June 2002, University of Iraklion,
Crete

Title: "Lattice points inside random ellipses"

March 2002, McGill University,
Montreal, Canada

Title: "Average decay of the Fourier transform and
distribution of lattice points in convex domains"

March 2002, AMS Special Session in
Harmonic Analysis

Title: "Average decay of the Fourier transform and
applications"

January 2002, Universita di
Milano-Bicocca

Title: "Applications of the average decay of the
Fourier transform of measures"

**2001 **(67)

December 2001, Georgia Institute of Technology

November 2001, Colloquium, Case
Western Reserve University

Title: "Combinatorics of convex sets and
applications"

November 2001, Seminar, University of
Wisconsin, Madison

Title: "Combinatorics of convex sets and
applications"

November 2001, Research visit at
McMaster University, Hamilton, Ontario

October 2001, Seminar, University of
Bristol, England

Title: "Combinatorial approach to orthogonal
exponentials"

September 2001, Colloquium ,
University of British Columbia,Vancouver, British Columbia,
Canada

Title: "Combinatorial aspects of convexity"

August 2001, Convex geometry
conference in Anogia, Crete

Title: "Various notions of dimension of
convex sets and applications"

May 2001, Partial Differential
Equations Seminar, University of Missouri-Columbia

Title: "Regularity of generalized Schrodinger
equations"

May 2001, Algebra Seminar, University
of Missouri-Columbia

Title: "Quadratic forms and the Steinhaus
tiling problem"

March 2001, Oscillatory Integrals and
Dispersive Equations, IPAM conference in Los Angeles, California

July 2001, Mt. Holyoke Harmonic
Analysis/ PDE AMS conference

Title: "Distribution of lattice points in convex
domains"

April 2001, University of
Milan-Bicocca

Title: "Extracting geometric information from
square functions"

March 2001, AMS Special Session in
Harmonic Analysis, Lawrence, Kansas

Title: "Distribution of lattice points inside
convex domains"

**2000 **(57)

December 2000, Meeting of the Canadian
Mathematical Society, Vancouver, British Columbia, Canada

Title: "Distribution of lattice points in convex
domains and the geometry of the Gauss map"

November 2000, University of
Wisconsin-Madison

Title: "Distribution of lattice points in convex
domains and the geometry of the Gauss map"

November 2000, McMaster University,
Hamilton, Ontario

Research collaboration with Eric Sawyer

November 2000, Banach space seminar,
University of Missouri-Columbia

Title: "Exponential bases and tiling- combinatorics
and the Fourier transform"

October 2000, Northwestern University,
Chicago, Illinois

Title: "Distribution of lattice points in convex
domains and related problems"

October 2000, Special Session in
Harmonic Analysis, San Francisco, California

Title: "Distribution of lattice points in convex
domains"

September 2000, Analysis seminar,
Washington University in St. Louis

Title: "Distribution of lattice points in convex
domains"

September -November 2000, Probability seminiar, University of
Missouri-Columbia

Title: "A brief introduction to the Kakeya problem
and related issues"

July 2000, Meeting of harmonic
analysts at El Escorial, Spain.

June 2000, Meeting of the Greek
analysts in Iraklion, Crete

Title: "Fourier bases and the associated
combinatorics"

June 2000, University of Iraklion, Crete

Title: *"Distribution of lattice points in
convex planar domains"*

June 2000, University of Milan-Bicocca

Title: *"Elementary applications of the
pigeon-hole principle in analysis"*

June 2000, Annual meeting of the
Italian harmonic analysts

Title: *"Distribution of lattice points in
convex domains"*

February 2000, University of
Missouri-Columbia

Title: *"The role of Gaussian curvature in
harmonic analysis"*

February 2000, Syracuse University

Title:* "Fourier bases, tiling, and the Erdos
Distance Problem"*

February 2000, McMaster University

*Joint research with E. Sawyer
*

**1999 **(44)

December 1999, University of Wisconsin-
Madison.

Title: *"Fourier bases, tiling, and the Erdos
Distance Problem"*

August 1999, University of Illinois at
Chicago

*Joint research with N. Katz facilitated by a
CRB Grant.*

August 1999, University of Illinois at
Chicago

Title: *"Fourier basis, orthogonality, and a
variant of Erd�s distance problem"*

July 1999, Joint meeting of the
American and Australian Mathematical Societies.

Title: *"Fourier basis, fractals, and the Erd�s
distance problem"*

June 1999, University of Milan

Title: "*Maximal averages over fractals"*

June 1999, Meeting of the Italian
Mathematical Society, Aosta, Italy

Title: *"Fourier basis and the Erd�s distance
problem"*

May 1999, Wright State University

Title: *"The role of curvature in harmonic
analysis"*

March 1999, McMaster University

Title: *"Averages over surfaces and related
problems"*

March 1999, Wright State University

* Joint research with S. Pedersen*.

March 1999, Indiana University Purdue
University Indianapolis

*Joint research with E. Sawyer.*

February 1999, University of
Maryland-College Park

Title: "*Lattice points, Fourier bases, and
related problems*"

January 1999, Conference on Singular
and Oscillatory Integrals in honor of Steve Wainger,

University of Wisconsin, Madison,
Wisconsin

Title: "*Lattice points, Fourier bases, and
related problems*"

**1998 **(35)

September 1998, AMS Special Session on
orthogonal polynomials and related problems,

DePaul University, Chicago, Illinois

Title: "*Smooth hypersurfaces of infinite type*"

August 1998, GAFA Conference, Kiel,
Germany

Title:* "L ^{p} improving properties of
measures supported on convex finite type hypersurfaces"*

July 1998, Visiting Research Fellowship, University of Milan, Milan, Italy

July 1998, University of Turin, Turin, Italy

Title:

June/July 1998, Visiting Research Fellowship, University of New South Wales, Sydney, Australia.

July 1998, Department of Mathematics Analysis Seminar, Macquarie University, Sydney, Australia

Title:

June 1998, Department of Mathematics, University of New South Wales, Sydney, Australia

Title:

April 1998, Dixieland Analysis Conference, Emory University, Atlanta, Georgia

Title:

April 1998, Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia

Title:

February 1998, Department of Mathematics, Johns Hopkins University, Baltimore, Maryland

Title:

February 1998, Department of Mathematics, Georgetown University, Washington,

District of Columbia

Title:

**1997 **(26)

Fall 1997, General Membership at the
Mathematical Sciences Research Institute, Berkeley, California

November 1997, Visiting Research
Fellowship, University of Naples, Naples, Italy

November 1997, Department of
Mathematics, University of Naples, Naples, Italy

Title: *"Scaling properties of infinitely flat
curves and surfaces"*

November 1997, Department of
Mathematics, University of Milan, Milan, Italy

Title: *"Scaling properties of infinitely flat
curves and surfaces"*

October 1997, Department of
Mathematics, University of Rochester, Rochester, New York

Title: *"Scaling properties of convex
hypersurfaces"*

September 1997, Mathematical Sciences
Research Institute, Berkeley, California

Title:* "Scaling properties of convex finite type
hypersurfaces"*

September 1997, Department of
Mathematics, Florida State University, Tallahassee, Florida

Title: *"Scaling properties of convex
hypersurfaces"*

September 1997, Integrable Systems
& Nonlinear PDE Seminar, Department of Mathematical
Sciences,

Indiana University Purdue University
Indianapolis, Indianapolis, Indiana

Title: *"Scaling properties of infinitely flat
curves and surfaces"*

May 1997, European Union HCM "Fourier Analysis Network" Harmonic
Analysis in Varenna Meeting, Varenna, Italy

Title: *"Averages over convex hypersurfaces"*

March 1997, Wright State University
Analysis Seminar, Dayton, Ohio

Title: *"Fourier transform, restriction
theorems, and scaling"*

March 1997, American Mathematical
Society Annual Analysis Conference in Auburn, Alabama

Title: *"Maximal averages over convex surfaces"*

**1996 **(15)

December 1996, Department of Mathematics,
University of Wisconsin, Madison, Wisconsin

Title: *"Maximal averages, convex hypersurfaces,
and rotational curvature in time"*

October 1996, Department of
Mathematics Colloquium, University of Cincinnati, Cincinnati,
Ohio

Title: *"The Fundamental Theorem of Calculus and
Beyond"*

July 1996, Department of Mathematics,
University of Turin, Turin, Italy

Title: *"Schulz's Theorem, mixed homogeneity,
and maximal operators"*

July 1996, Department of Mathematics,
University of Naples, Naples, Italy

Title: *"Maximal operators in Harmonic
Analysis"*

June 1996, Department of Mathematics,
McMaster University, Hamilton, Ontario, Canada

Title: *"Maximal averages over mixed homogeneous
surfaces"*

**1995** (10)

December 1995, Department of Mathematics,
University of Wisconsin, Madison, Wisconsin

Title:* "Oscillatory integrals with homogeneous
phases and maximal averages over surfaces"*

November 1995, American Mathematical
Society Conference in Kent, Ohio, Special Session on

Harmonic Analysis and Applications,
Kent State University, Kent, Ohio

Title: *"Averaging and maximal averaging
operators associated to homogeneous hypersurfaces"*

February 1995, Analysis Seminar, University of Toronto, Toronto,
Ontario, Canada

Title: *"Maximal operators and oscillatory
integrals associated to finite type hypersurfaces"*

**1994** (7)

September 1994, Harmonic Analysis Seminar,
McMaster University, Hamilton, Ontario, Canada

Title: *"(L ^{p},L^{q}) mapping
properties of averaging operators associated to homogeneous
hypersurfaces"*

May 1994, Harmonic Analysis Seminar, McMaster University

Title:

June 1994, Functional Analysis Seminar, Technion, Haifa, Israel

Title:

June 1994, Mathematics Colloquium, University of Naples, Naples, Italy

Title:

May 1994, Analysis Seminar, UCLA, Los Angeles, California

Title:

**1993 **(2)

November 1993, Harmonic Analysis Seminar,
McMaster University

Title: *"A restriction theorem for operators
associated to homogeneous manifolds in codimension two"
*

**1991 **(1)

March 1991, Classical Analysis Seminar, UCLA,
Los Angeles, California

Title:* "Maximal operators associated to families
of flat curves in the plane"*

August 2023, A lecture series at the Kent
State Informal Analysis Seminar

Title: Geometric measure theory and applications to data
science

July 2023, A lecture series at the University
of Harbin, China

Title: Geometric measure theory and applications to data
science

February 2017, A lecture series on the
Falconer conjecture at the Louisiana State University.

Title: Finite point configurations and exponential bases
and frames

August 2012, A lecture series on multilinear
operators and geometric measure theory at Chungbuk University,
South Korea

Title: A multi-linear approach to finite point
configurations

May 2012, A lecture series on application of
harmonic analysis to geometric combinatorics at CANT2012
conference in CUNY, New York

Title: From discrete to continuous and back

October 2008, A lecture series on interaction
of harmonic analysis, geometric combinatorics and additive
number theory at Baylor University (three lectures)

Title: Analytic, number theoretic and combinatorial
aspects of the theory of finite point configurations

November 2006, A lecture series on harmonic
analysis in vector spaces over finite fields at the University
of Bristol (four lectures)

Title: Erdos and Falconer in vector spaces over finite
fields

May 2006, CUNY, New York, CANT 2006 (three
lectures)

Title: "Three lectures on analytic, combinatorial and
number theoretic aspects of incidence theory"

June 2002, University of Padova, Minicorsi di
Analisi Matematica (three lectures)

Title: "Geometric combinatorics and applications to
analysis"

July 1998, A series of talks at the University
of Milan on avergaing operators over hypersurfaces (four
lectures)

Title: Stein's conjecture, scaling and maximal averages
over surfaces

__PUBLICATIONS:__

__Published Papers and Papers Accepted for
Publication:__

**The published papers are listed first,
organized by year of publication. Accepted papers are listed
below, immediately following the published papers.
**

__2022
(144)
__

Dot products in *(**with
McDonald, B.; Sun, M), Discrete
Math.* 346 (2023), no. 1,

Uniform distribution and geometric incidence theory,
(with A. Gafni and E. Wyman), *J.
Math. Anal. Appl.* 517 (2023), no. 1

__2022 (142)
__

Microlocal decoupling
inequalities and the distance problem on Riemannian
manifolds, Amer. J. Math, 144 (2022), no. 6, 1601-1639.

On *, (with A. *Greenleaf and K. Taylor), *Mathematika* 68 (2022), no. 1, 163-19

Fourier frames
for surface-carried measures, (with Lai, Liu and Wyman)
*Int. Math. Res.
Not. IMRN* 2022, no. 3, 1644-1665.

Simplex Averaging Operators: Quasi-Banach and Lp-improving Bounds in Lower Dimensions, (with E. Palsson and S. Sovine), J. Geom. Anal. 32 (2022), no

** 2021 **(138)

Rigidity, graphs and
Hausdorff dimension, (wtih N. Chatzikonstantinou,
S. Mkrtchyan, and J. Pakianathan), *Combinatorial and additive
number theory IV, *73–106, Springer Proc. Math. Stat.,
347

Repeated distances and dot products in finite fields*,
(with C. Wolf), **Operator theory and
harmonic analysis—OTHA 2020. Part I. New general trends and
advances of the theory, *243–257, Springer
Proc. Math. Stat 357.

__ __

Cycles of arbitrary length in distance graphs on
vector spaces over finite fields, (Russian*),
(with G. Jardine and B. McDonald), **Tr.
Mat. Inst. Steklova* 314 (2021), Analiticheskaya
i Kombinatornaya Teoriya Chisel, 31–48.

Sums of Powers in Large Finite Fields: A Mix of
Methods*, (**with
Bergelson, Vitaly and Best, Andrew)*__,
__*Amer.
Math. Monthly* 128 (2021), no. 8, 701–718.

Weyl Law Improvement for Products of Spheres, (with
E.
Wyman)__,
__*Anal.
Math.* 47 (2021), no. 3, 593–612.

An improved result for Falconer's distance set
problem in even dimensions*, (*__with
Du, Xiumin; Ou,
Yumeng; Wang,
Hong; Zhang,
Ruixiang ) __*Math.
Ann.* 380 (2021), no. 3-4, 1215–1231.

Configuration sets with nonempty interior, (Greenleaf,
Allan; Iosevich,
Alex; Taylor,
Krystal), *J.
Geom. Anal.* 31 (2021), no. 7, 6662–6680.

On restriction estimates for the zero radius sphere over
finite fields, (with Koh,
Doowon; Lee,
Sujin; Pham,
Thang; Shen,
Chun-Yen), *Canad.
J. Math.* 73 (2021), no. 3, 769–786.

Existence of similar point configurations in thin
subsets of Euclidean space, (with A. Greenleaf and M.
Mkrtchyan), *Math.
Z.* 297 (2021), no. 1-2, 855-865.

__
__

**
2020 **(128)

__Falconer-type estimates for dot products, (with S.
Senger), Bull.
Hellenic Math. Soc. 64 (2020), 98–110.__

**A new bound
for the Erdős distinct distances problem in
the plane over prime field***s,
(with D. Koh, T. Pham. C. Shen and L. Vinh). **Acta Arith.* 193 (2020), no. 2, 165**-**174.

**New
bounds for distance-type problems over prime
fields, **

__ On
Falconer's distance set problem in the plane,
(with L. __Guth,

**2019 **(123)

__Finite trees inside thin subsets of
Euclidean space, (with K. Taylor) accepted for publication by
the Proceedings of the Analysis and Operator Theory conference
in Rostov, Russia.
__

__Embedding distance graphs in finite field
vector spaces, (with H. Parshall), __ *J.
Korean Math. Soc.* 56 (2019), no.
6, 1515�1528.

Equilateral triangles in subsets of Euclidean space of large Hausdorff dimension, (with B. Liu) Israel Math Journal, May, 2019, Volume 231, issue 1, pages 123-137.

On the quotient set of the distance set, (with D. Koh and H. Parshall), Moscow Journal of Combinatorics and Number Theory 8 (2019), no. 2, 103�115.

What is Falconer's conjecture? Notices of the AMS, March 2019.

Fourier analysis and Hausdorff dimension, by Pertti Mattila, Mathematical Intelligencer, March, 2019, Volume 41, Issue 1, 83-86.

Pinned distance problem, slicing measures and local smoothing estimates, (with B. Liu), Transactions of the AMS, volume 371, no. 6, 4459-4474.

Maximal
operators: scales, curvature and the fractal dimension,
(with B. Krause, E. Sawyer, K. Taylor and I. Uriarte-Tuero), *Anal.
Math.* 45 (2019), no.
1, 63-86.

__Tight
wavelet frame sets on finite vector spaces, (with C.
Lai and A. Mayeli), The Journal of Applied and
Computational Harmonic Analysis, volume 46, issue 1.
__

2018

Finite point
configurations in the plane, rigidity and Erdos problems
(with J. Passant) Tr. Mat. Inst. Steklova 303 (2018),
142-154.

Gabor orthogonal bases on
convexity (with A. Mayeli), *Discrete
Anal.* 2018, Paper No. 19, 11 pp.

Wavelet
decomposition and bandwidth of functions defined on vector
spaces over finite field*s, **(with A. Liu, A.
Mayeli and J. Pakianathan), **Bull.
Hellenic Math. Soc.* 62 (2018), 80–93.

Tiling, circle packing and exponential sums over finite fields, (with C. D. Haessig, A. Iosevich, J. Pakianathan, S. Robins and L. Vaicunas), Analysis Mathematica, 44 (2018), no. 4, 433-449.

Distances from points to planes, (with P. Birklbauer and T. Pham), Acta Arithmetica 186 (2018) no. 3 219-224.

On discrete values of bilinear forms, (with O. Roche-Newton and M. Rudnev) Mat. Sb. 209 (2018), no. 10, 71-88.

Direction sets,
Lipschitz graphs and density, (with J. Pakianathan),
Bull. Hellenic Math. Soc. 62 (2018) 61-65.

** 2017 **(106)

Tiling sets
and spectral sets over finite fields, (with Aten,
C.; Ayachi,
B.; Bau,
E.; FitzPatrick,
D.; Liu,
H.; Lott,
A.; MacKinnon,
I.; Maimon,
S.; Nan,
S.; Pakianathan,
J.; Petridis,
G.; Rojas
Mena, C.; Sheikh,
A.; Tribone,
T.; Weill,
J.; Yu,
C.)
*J. Funct. Anal.* 273 (2017), no. 8, 2547-2577.

On necklaces
inside thin subsets of ${\Bbb R}^d$, (with A. Greenleaf
and M. Pramanik), Math Research Letters, 24 (2017), 347-362.

A
two-parameter finite field Erdős-Falconer distance problem*,
**(with
P. Birklbauer) Bull. Hellenic Math. Soc. *61 (2017),
21-30

Elementary methods
for incidence problems in finite fields, (with J.
Cilleruelo, B. Lund, Ben, O. Roche-Newton and M. Rudnev), Acta
Arith. 177 (2017), no. 2, 133-142.

The Fuglede
conjecture holds in ${\Bbb Z}_p \times {\Bbb Z}_p$ (with
A. Mayeli and J. Pakianathan), Anal. PDE 10 (2017), no. 4.

The square root law
and structure of finite rings, (with B. Murphy and J.
Pakianathan), Moscow Journal of Combinatorics and Number Theory,
Volume 7, Issue 1, (2017).

Group actions and geometric combinatorics in 𝔽dq, (with M. Bennett, D. Hart, Derrick, J. Pakianathan and M. Rudnev), Forum Math. 29 (2017), no. 1, 91-1

(99)

2016

On angles
determined by fractal subsets of Euclidean space, (with M.
Mourgoglou and E. Palsson), volume 23, number 6, (2016).

Sharpness of Falconer's $\frac{d+1}{2}$ estimate, (with Steven Senger), Annales Academic Scientiarum Fennicae, volume 41, (2016).

Falconer distance problem, additive energy and Cartesian products, (with B. Liu), Annales Academic Scientiarum Fennicae, volume 41, (2016).

Finite chains inside thin subsets of ${\Bbb R}^d$, (with M. Bennett and K. Taylor), Analysis and PDE, volume 9, no. 3, (2016).

Long paths in the
distance graph over large subsets of vector spaces over finite
fields, (with M. Bennett, J. Chapman, D. Covert, D. Hart
and J. Pakianathan), Journal of Korean Mathematical Society,
volume 53, pages 115-126 (2016).

Intersections of
sets, diophantine equations and Fourier analysis, (with
Suresh Eswarathasan, Alex Iosevich, Krystal Taylor), Journal
d'Analyse, volume 128, pages 159-178 (2016).

Sets
of finite perimeter and geometric variational problems. An
introduction to geometric measure theory [book review of
MR2976521]. Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 1, 167**-**171.

**2015 **(92)

A group-theoretic
viewpoint on Erdős-Falconer problems and the Mattila integral,
(with A. Greenleaf, B. Liu and E. Palsson), Rev. Mat. Iberoam.
31 (2015), no. 3, 799-810.

Multi-linear
generalized Radon transforms and point configurations,
(with L. Grafakos, A. Greenleaf and E. Palsson), Forum Math. 27
(2015), no. 4, 2323-2360.

Areas of triangles
and Beck's theorem in planes over finite fields, (with M.
Rudnev and Y. Zhai), Combinatorica 35 (2015), no. 3, 295-308

On volumes
determined by subsets of the Euclidean space, (with A.
Greenleaf and M. Mourgoglou), Forum Mathematicum, volume 27,
issue 1, (2015).

Paley-Wiener
spaces and applications, (with A. Mayeli) J. Funct. Anal.
268 (2015), no. 2, 363-375.

**2014 **(87)

Decay of the Fourier transform, (with Elijah Liflyand), Analytic and geometric aspects. Birkhauser/Springer, Basel, (2015).

Three-point
configurations determined by subsets of the two-dimensional
finite plane via the Elekes-Sharir paradigm, (with M.
Bennett and J. Pakianathan) Combinatorica 34 (2014), no. 6,
689-706

Theory of
dimension for large discrete sets and applications, (with
M. Rudnev and I. Uriarte-Tuero), Math. Model. Nat. Phenom. 9
(2014), no. 5, 148-169.

Sharpness of
Falconer's estimate and the single distance problem in Z_q^d,
(with S. Senger), Combinatorial and additive number theory-CANT
2011 and 2012, 63-77, Springer Proc. Math. Stat., 101, Springer,
New York, (2014).

**2013 **(83)

Distance graphs in
vector spaces over finite fields. *Recent advances in
harmonic analysis and applications,* (with
Hart,
Derrick; Koh,
Doowon; Senger,
Steven; and
Uriarte-Tuero, Ignacio) 139–160, Springer
Proc. Math. Stat., 25, *Springer, New York,* 2013.

Restricted convolution inequalities, multi-linear operators and applications, (with D. Geba, A. Greenleaf, E. Sawyer and E. Palsson), Math Research Letters, volume 20, No. 4 (2013).

Geometric
configurations in the ring of integers modulo p^l, (with
D. Covert and J. Pakianathan), volume 61, issue 5, (2013).

Size of orthogonal
sets of exponentials on the disk, (with M. Kolountzakis),
Revista Iberoamericana, volume 29, 739-747 (2013).

Periodicity
of the spectrum in dimension one, (with M. Kolountzakis),
Analysis and PDE, volume 6, no. 4 (2013).

Multi-parameter projection theorems with applications to sums-products and finite point configurations in the Euclidean setting, (with B. Erdogan and D. Hart), (Springer volume in honor of Kostya Oskolkov's 65th birthday).

**
2012 **(77)

Geometric configurations in the ring of integers
modulo p^l, (with D. Covert and J. Pakianathan), *Indiana Univ. Math. J.* 61 (2012), no. 5, 1949–1969.

Three point
configuration, a bilinear operator and applications to
discrete geometry, (with A. Greenleaf), Analysis & PDE
5-2 (2012), 397-409.

Pinned distance sets,
k-simplices, Wolff's exponent in finite fields and sum-product
estimates, (with Jeremy Chapman, M. Burak Erdoğan, Derrick
Hart, Alex Iosevich and Doowon Koh), Mathematische Zeitschrift,
*Math. Z.* 271
(2012),
no.
1-2, 63-93.

On the Mattila-Sjolin theorem, (with M. Mourgoglou and K. Taylor), Annales Academic Scientiarum Fennicae, 37 no. 2, (2012).

On sets of directions
determined by fractal subsets of the Euclidean space, (with
M. Mourgoglou and S. Senger), Journal D'Analyse, 116 no. 1,
(2012).

**
2011 **(72)

Lattice points close
to families of surfaces, non-isotropic dilations and
generalized Radon transforms, (with K. Taylor), New York
Journal of Mathematics, 17, 1-19, (2011).

Fourier integral operators, fractal sets and the regular value theorem, (with S. Eswarathasan and K. Taylor), Advances in Mathematics, 228, (2011).

An analog of the
Furstenberg-Katznelson-Weiss theorem on triangles in sets of
positive density in finite field geometries, (with D.
Covert, D. Hart, S. Senger and I. Uriarte-Tuero), Discrete Math.
311, no. 6, 423-430, (2011).

On application of Guth-Katz theorem, (with M. Rudnev and O.
Roche-Newton), Mathematics Research Notices 18, no. 4, 1-7.

On directions determined by subsets of vector spaces over finite fields, (with H. Morgan and J. Pakianathan), Integers, 11, (2011).

Erdos
distance problem, (with J. Garibaldi and S. Senger), AMS
Student Library Series, 56, (2011).

**2010**
(65)

A universal Stein-Tomas restriction estimate for measures in three dimensions, (with S. Roudenko), Festschrift dedicated to Mel Nathanson's 60th birthday, Springer, (2010) 171-178.

Extension theorems for
paraboloids in the finite field setting, (with D. Koh),
Mathematische Zeitschrift, 266, (2010) no.2 471-487.

Extension
theorems for spheres in the finite field setting, (with D.
Koh), Forum Math. 22 (2010), no. 3, 457-483.

The discrepancy of a
needle on a checkerboard II, (with M. Kolountzakis) Unif.
Distrib. Theory 5 (2010), no. 2, 1-13.

Sets
with integral distances in finite fields, (with I.
Shparlinski and M. Xiong) Trans. Amer. Math. Soc. 362 2010, no.
4, 2189--2204.

**2009**
(59)

On
rapid generation of ${\rm SL}\sb 2(\Bbb F\sb Q)$, (with J.
Chapman) Integers 9 (2009), A4, 47-52.

Freiman's
theorem, Fourier transform, and additive structure of
measures, (with M. Rudnev), Journal of the Australian
Mathematical Society, 86, 2009, 97-109.

**2008**
(55)

Orthogonal systems in vector spaces over finite fields, (with S. Senger), Electronic J. of Combinatorics, volume 15, December (2008).

Powder diffraction from a combinatorial and analytic viewpoint,
(with M. Rudnev), Integers, volume 8, (2008).

Sums and products
in finite fields: an integral geometric viewpoint, (with
D. Hart), Contemporary Mathematics, volume 464, (2008).

*Fourier analysis and geometric
combinatorics **Topics in mathematical analysis, *
321--335, Ser.
Anal. Appl. Comput., 3, *World Sci. Publ., Hackensack,
NJ,* 2008.

Ubiquity of
simplexes in vector spaces over finite fields, (with D.
Hart), Analysis Mathematica, volume 34 (2008).

**2007**
(47)

A view from the top: analysis, combinatorics and number theory,
(book), AMS Student Library Series, volume 39.

**2006**
(40)

Combinatorial
complexity of convex sequences, (With S. Konyagin, M. Rudnev
and V. Ten), Journal of Discrete and Computational Geometry,
vol. 35, no. 1, (2006), pages 143-158.

2005
(38)

** 2004** (35)

Fourier analysis and convexity. Edited by Luca Brandolini,
Leonardo Colzani, Alex Iosevich and Giancarlo Travaglini. Applied
and Numerical Harmonic Analysis. *Birkhauser Boston,
Inc., Boston, MA*

Lattice
points inside random ellipsoids, (with S. Hofmann and D.
Weidinger), Michigan Math. J. 52 (2004), no. 1, pages 13-21.

Distance sets of well-distributed planar sets, (with I.
Laba), Journal of Discrete and Computational Geometry, vol.
31 no. 2, pages 243-250.

** 2002** (25)

** 2001** (21)

** 2000** (17)

** 1999** (15)

** 1998 **(8)

** 1997 **(6)

** 1996 **(5)

*Averages
over homogeneous hypersurfaces, Forum Mathematicum, Volume 8
(1996), Number 2, pp. 219-235.*

** 1995 **(2)

** 1994 **(1)