StemForAll 2025

SpongeBob


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