__StemForAll
2025__

**Organizers:
Alex Iosevich (University of Rochester) and Azita Mayeli
(CUNY) **** **

**Introduction:** Welcome to StemForAll2025 summer workshop. All
the interested Rochester area 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. In 2025, the program in
Rochester will be organized by **Alex Iosevich** (UR), **Steven
Kleene** (UR) and **Azita Mayeli** (CUNY).

**History of the program:** StemForAll has been running at the
University of Rochester since 2018. In one form or another this
program has existed at the University of Rochester and University of
Missouri since 2001. Many of its participant have since obtained
Ph.Ds in mathematics and related fields and have become successful
researchers. The links to the previous programs can be found here.

**Expansion:** The StemForAll program is expanding in 2025. In
addition to the annual program we have been running in the Rochester
area for several years, analogous programs are going to run at the
following institutions:

Missouri State University (**Steven Senger**)

Virgina Tech (**Eyvindur Palsson**)

Ohio State University (**Krystal Taylor**)

The StemForAll Team consists mathematicians who have committed to
running a two-week StemForAll undergraduate research program at
their home institutions during Summer 2025. The members of the team
are going to create a joint database of research problems and other
research materials, and share those with all the other affiliates.

**Rochester StemForAll location and time:** StemForAll2025 in the
Rochester area is going to take place in July/August 2025 at a time
and location yet to be determined.

**Structure of the workshop:** In 2025, StemForAll in Rochester
will be mainly (but not entirely) dedicated to the pure and applied
aspects of signal recovery. The basic problem is to send a signal
via its Fourier transform and then recover this signal from
incomplete information. The pure aspects of this problem touch upon
Fourier analysis, probability theory, information theory, complexity
theory and much more. The applied aspects include back-filling time
series, forecasting, recurring transmissions, and this is just the
beginning. The __exact location__ of the program will be
determined in the coming weeks.

__Workshop Projects: __

**1)**** ****Exact
Signal Recovery**

**Project
supervisors:** Alex Iosevich and
Azita Mayeli

**Research
meeting location: **TBD

**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:** TBD

**2) ****Fourier Analysis and Recovery of Missing Values
in Times Series**

**Project supervisors:** Will Burstein, Alex
Iosevich, Azita Mayeli, and Hari Nathan

**Research meeting location:**
TBD

**Project
description: **In a paper in preparation, the project
supervisors showed that the performance of virtually any
reasonable time series forecasting engine can be improved,
with high probability, by judiciously **
**filtering out a certain number of small Fourier coefficients at
the end of the forecast. The purpose of this project is to optimize
and streamline this process. We will also make an effort to unify
our approach with the classical techniques of exact signal recovery
that will be explored by the Exact Signal Recovery research group.

**Project
participants:** TBD

**3)** **Election Forecasts and Neural Networks**

**Project supervisors:** Alex Iosevich and Hari Nathan

**Research meeting location:**
TBD

**Project description:** We are going to examine the
polling data preceding the November 5, 2024 Presidential
Election and design neural network models to forecast
the outcome in terms of the popular vote, the number of
electoral votes and the outcome of the election. We
shall then compare the performance of our models against
the actual outcome of the elections.

**Project
participants:** TBD

**4) Sampling on Manifolds and Fourier Uncertainty
Principle **

**Project supervisors: **Alex Iosevich, Azita Mayeli
and Steven Kleene

**Research
meeting location:** TBD

**Project
description: **In a paper in
preparation, Iosevich,
Renfrew and Wyman are studying the problem
of how many random samples are needed to
reconstruct a band-limited function on a
compact Riemannian manifold without a
boundary. They are studying the stability of
the recovery process in terms of the
smallest singular values of the underlying
matrix. In this project, we are going to
conduct extensive numerical experiments
designed to get a feel for this process on
concrete Riemannian manifolds. We are also
going to study the Fourier uncertainty
principle on Riemannian manifolds, following
up on a recent paper on this topic by
Iosevich, Mayeli and Wyman.

**Project participants:** TBD

**5)
Improving numerical techniques for
simulating active matter and pattern
formation with moving boundaries**

Project supervisors: Alice Quillen
and Nathan Skerret

**Research meeting location: **Bausch
and Lomb 424

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: TBD

**6) Sales
modeling with economic indicators **

Project supervisors: Alex Iosevich,
Azita Mayeli, and TBD

**Research meeting location: **TBD

**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: **TBD

**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

7)** ****Numerical
solutions for partial differential
equations**

**Project supervisors:** Alex Iosevich
and Kunxu Song

**Research meeting location: **TBD

**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:** TBD

**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