Welcome to StemForAll2024 summer workshop. All the interested University of Rochester students are welcome to participate. The registration process is only used to assign the students to suitable projects. The main idea behind the workshop is to share the research we are doing with undergraduate students for the purpose of familiarizing them with research methods and techniques. Quite often research papers result from these discussions, but the main emphasis is on learning and the creative process.

Organizers: Alex Iosevich and Azita Mayeli

StemForAll2024 Workshop Instructional Team: Matthew Dannenberg, Gabe Hart, Alex Iosevich, Steven Kleene, Anuraag Kumar, Azita Mayeli, Svetlana Pack, Alice Quillen, Nathan Skerret, Stephanie Wang, and Nathan Whybra

Dates: July 29 - August 9, 2024

Structure of the workshop: The workshop is going to consist of supervised research projects and series of lectures designed to help gain the necessary background as you are working on your projects. The exact topics of the lecture series will be determined in the coming weeks. The exact topics for the research projects will be selected based on your interests and preferences.

This workshop is partly a culmination of undergraduate research activities that have transpired during the academic year. Once the workshop is over, the research projects are likely to continue into the Fall 2024 semester and beyond.

Registration process: Please fill out an on-line registration form at the following link. The students at all the Rochester area colleges and universities are welcome to register.

Dates and locations:

The program is going to run from July 29 until August 9 on the 11th floor of Hylan Bldg at the University of Rochester  

Preliminary schedule:

Week 1:

Discrete Fourier Analysis mini-course: 8 a.m. - 9.30 a.m. (location to be announced)

Probability mini-course: 10.00 a.m. -  11.30 p.m. (location to be announced)

Lunch break: 11:30 a.m. - 2.00 p.m.

Meeting of the research groups: 2.00 p.m. - 4.00 p.m.

Dinner break: 4.00 p.m. - 7.00 p.m.

Python coding groups: 7 p.m. - 9 p.m.

Week 2:

Research groups meeting on their own, with or without instructors: 8.00 a.m. - 9.00 a.m.

Research groups meeting with project supervisors: 9:00 a.m. - 11:00 a.m.

Lunch break: 11:00 a.m. -1.30 p.m.

Research group meetings with project supervisors: 1.30 p.m. - 3.00 p.m.

Participants working individually and in small groups: 3.00 p.m. - 4.00 p.m.

Dinner break: 4:00 p.m. - 7.00 p.m.

Evening regroup with supervisors: 7.00 p.m. - 8.00 p.m.

Workshop Projects:
Exact signal recovery

Project supervisors: Alex Iosevich and Azita Mayeli

1) Project description: Suppose that a signal of length N is transmitted via its discrete Fourier transform and some of the signal is lost in the transmission due to noise or interference. Under what conditions is it possible to recover the original signal exactly? This innocent looking question quickly leads to some interesting techniques and ideas from analysis, combinatorics and other areas of mathematics. We are going to investigate these types of questions from both the theoretical and computational points of view.

Project participants: Karam Aldahleh, Karina Gurevich, Josh Iosevich, Jonathan Jaimangal, Kelvin Ngyuen, Aidan Rohrbach, Nate Shaffer, Terrence Wong,

Things to learn (or review) before the workshop: Discrete Fourier transform on integers modulo N, Fourier inversion, Plancherel, basic Gauss sums, Fourier transform of the indicator function of the circle, Fourier transform of the indicator function of a random set, python packages that compute the discrete Fourier transform.

Reading materials: i) Notes on the Fourier transform by Lazslo Babai, ii) The paper by Hart, Iosevich, Koh and Rudnev on geometric combinatorics in vector spaces over finite field, and iii) The paper on signal recovery by Iosevich and Mayeli.

2) Buffon Needle Problem

Project supervisors:
Gabe Hart and Steven Kleene

Project description: This project is continuing from last summer. The question is, which convex domain K in d-dimensional Euclidean space with a boundary with a fixed (d-1)-dimensional Hausorff content maximizes the Buffon probability? Here the Buffon probability p(K,r) is the probability that if one end of a needle of length r lands in K with uniform probability, then the other end also lands in K. Last summer, William Hagerstrom, Gabriel Hart, Tran Duy Anh Le, Isaac Li, and Nathan Skerett essentially resolved this question in two dimensions. They proved that given any convex set K in the plane where the length of the boundary is equal to 2 pi, there exists a threshold r_0 such that if r<r_0 and K is not the unit disk D, then p(K,r)<p(D,r). The purpose of this year's project is to extend this result to higher dimensions.

Project participants: William Hagerstrom, Gabe Hart, and Philip Olapade

Things to learn (or review) before the workshop: Basic probability, integral geometry, convexity-based inequalities, and study the results on the Buffon Needle Problem produced during StemForAll2023.

Reading materials: i) Integral Geometry and Geometric Probability, by Luis Santalo (book) ii) The paper based on StemForAll2023 Buffon Needle results (coming soon)

3) Automated theorem proving

Project supervisors:
Alex Iosevich, Azita Mayeli, Stephanie Wang, Yifan Zhu

Project description:
The Automated Theorem Proving (ATP) research group will focus on first understanding, then developing computer programs that can prove mathematical theorems automatically. We plan to tackle the first few chapters of "Introduction to Univalent Foundations of Mathematics," which introduces a new way of thinking about mathematics, emphasizing how objects are the same (or equivalent) rather than just focusing on their properties. The group's goal is to use computers to navigate and validate the theories and exercises in these chapters, helping to advance our understanding of how these foundational concepts can be applied and verified using technology. Coding will be done in Python, and use of ChatGPT is welcome and even encouraged so far as the programmer understands the code produced.

Project participants: Fatimah Almuallim, Jessica Chen, James Choe, Ioanna Geba, Zhifeng Guo, Xinliang He, Yunhui Li, Aidan Lieberman, Shouyi Lin, Zacharay Tan, Ruzicka Vuckovic, Stephanie Wang

Things to learn (or review) before the workshop: Python programming and read up on automated theorem proving.

Reading materials: i) Please read the following notes  ii) Please read the following book

4) Kolmogorov complexity and Hausdorff dimension

Project supervisors: Alex Iosevich, Azita Mayeli and Svetlana Pack

Project description: The purpose of this project is to understand the emerging connections between Kolomogorov complexity and Hausdorff dimension, with applications to configuration problems, complexity of graphs and machine learning.

Project participants: Noah Ernst, Adarsh Kumar, Charlie Li

Things to learn (or review) before the workshop: Read up on Kolomogorov complexity and fractal dimension.

Reading materials: i) A book on Kolmogorov complexity

5) Numerical solutions for partial differential equations

Project supervisors: Alex Iosevich and Kunxu Song

Project description: The group will use deep learning methods to investigate solutions of various partial differential equations. In particular, they will investigate how to solve the high latitude heat equation using a neural additive model. The group will also work on other SPDE related problems if time permits.

Project participants: Yuning Ren, Kunxu Song, Xiaoya Tan, Jingwen Xu, Xianquan Yan

Things to learn (or review) before the workshop: Basic theory of partial differential equations, probability, fundamentals of stochastic analysis, and python programming.

Reading materials: Coming soon

6) Graph theory and cycle double-covers

Project supervisors: Gabe Hart and Alex Iosevich

Project description: A cycle double-cover of a graph G is a set of cycles in G such that every edge of G is included in exactly 2 of the cycles. The cycle double-cover conjecture states that every bridgeless graph has a cycle double-cover. We will investigate this conjecture and related problems using both theoretical and computational methods.

Project participants: Nicholas Arnold, Fardowsa Abdulle, Gabe Hart, Aidan Rohrbach, and BingKun Ye

Things to learn (or review) before the workshop: Basic graph theory, definition of the cycle double-cover iv)

Reading materials: i) Wikipedia graph theory article, ii) Cycle double cover wikipedia article, iii) Matroid theory,

7) Math education modeling methods

Project supervisors: Alex Iosevich, Azita Mayeli, Anuurag Kumar and Stephanie Wang

Project description: At present, the United States severely underperforms in mathematics relative to its global standing, leading to countless attempts to aid STEM students. Lesser studied, however, is pedagogy at the undergraduate level, and the factors that go into attracting and retaining math major students. In this group, we will explore the variety of factors that contribute to the undergraduate mathematics experience through a first-generation lens, including, but not limited to: allocation of university resources, available mathematical support, community openness, perceived mathematical stigma and career trajectory, etc. Students in this group can expect to do mathematical modeling of demographics and statistical analysis, as well as learn how to apply quantitative measurements to subject data (interviews, surveys, etc.). Coding will be done in Python and/or R, and use of ChatGPT is welcome and even encouraged so far as the programmer understands the code produced.

Project participants: Ayse Bicacki, Anurag Kumar, Stephanie Wang, Shuyu Zhang, Kangcheng Zhao, Xinrui Zhao

Things to learn (or review) before the workshop: Read up on challenges faced by first-generation college students 

Reading materials: i) Post-secondary success and first-generation students, ii) Pre-college experience and effect on first-generation students

8) Random walks and finite graphs

Project supervisors:
Alex Iosevich, Matthew Dannenberg, and Anuraag Kumar

Project description: We are going to study random walks on graphs using Markov chain methods. The goal is to determine accurate distributions of hitting times.

Project participants: Yujia Ju, Anuurag Kumar, and Yiling Zou

Things to learn (or review) before the workshop: Basic probability and theory of random walks

Reading materials: Coming soon

9) Erdos distance problem on manifolds

Project supervisors: Alex Iosevich, Steven Kleene and Nathan Skerett

Project description: The classical Erdos distance problem asks for the smallest possible number of distances determined by n points in Euclidean space in dimensions two and higher. In this project we are going to investigate this problem on Riemannian manifolds. The starting point for this investigation is Nathan Skerrett's undergraduate honors thesis. 

Project participants: Lily Stolberg, June Terzioglu and Nate Shaffer

Things to learn (or review) before the workshop: Basic combinatorics, fundamental results on the Erdos distance problem, Riemannian geometry

Reading materials: i) Erdos Distance Problem by Garibaldi, Iosevich and Senger, ii) Notes on Differential Geometry by Desernno, iii) Nathan Skerett's honors thesis

10) Improving numerical techniques for simulating active matter and pattern formation with moving boundaries

Project supervisors:
Alice Quillen and Nathan Skerret

Project description:
Active matter and pattern formation can be described with PDEs.  The behavior of the system can be affected by the boundaries that confine the continuous medium.  Our goal is to develop numerical techniques based on particle based or finite element methods for exploring the behavior of confined active media in 2D.  One possibility is to generalize the Immersed Boundary method so that it can be used for a more diverse set of PDEs than hydrodynamics.

Associated lectures could be on active matter and simulation techniques for active matter,  pattern formation models. particle based methods and grid based methods for PDEs and immersed boundary methods.

Project participants:
Aaron Iosevich, Roshan Mehta and Allen Shao

Things to learn (or review) before the workshop: Coming soon

Reading materials: Coming soon

11) Sales modeling with economic indicators

Project supervisors:
Alex Iosevich, Azita Mayeli, and Nathan Whybra

Project description: We are going to build and test neural network models with economic indicator regressors to effectively predict future sales in retail. A variety of neural network models will be built using tensorflow, keras, facebook prophet and others. Theoretical aspects of this problem will be considered as well.

Project participants: Hashem Alomari, Yiqin He, Sylvia Liu, Xavier Jiang, Shimo Li, Adam Sun, Yicheng Shi, Josih Torres, Joy Xiang, Binbo Xu, Jonathan Zhang, Yuxuan Zhao, Zhechao Zhao, and Daiming Zhou

Things to learn (or review) before the workshop: Basics of python, including numpy and pandas, and basic usage of tensorflow and related packages. 

Reading materials: i) Python tutorial  ii) Tensorflow tutorials

12) Forecasting medical data using neural networks

Project supervisors:
Alex Iosevich, Azita Mayeli and Svetlana Pack

Project description:
We are going to work with large swaths of medical data, including EEG, seizures and others, and look for identifiable patterns using neural network analysis and more elementary statistical techniques.

Project participants: Nadia Lab Hab, Ji Woong Hong, Alex Novak, Aabha Pandit, Mishnu Pendri, Aidan Lieberman, Yujun Sun, Kangmin Sung, Yi Wu, and Haotian Yang

Things to learn (or review) before the workshop: Basics of python, including numpy and pandas, and basic usage of tensorflow and related packages. 

Reading materials: i) Python tutorial  ii) Tensorflow tutorials