# Projects 2024

Add Headings and they will appear in your table of contents.

Here is a tentative incomplete list of some of the projects proposed by mentors for this summer. You do not need to choose a project in your application. The committee will coordinate with mentors and match with students.

Predicting win probabilities from NFL and NBA data by Prof. Ted Westling

Problems inspired by physics and probability but tackled using a mix of algebra and combinatorics by Prof. Owen Gwilliam

I have two possible projects: (1) Large scale biobank data are often used to discover important genetic variants. Since individuals participating in the biobank are typically not representative of the general population, we need to know the probability of participation to make valid discoveries. In this project, you will explore ways to estimate the probability that an individual participates in a biobank study; (2) A large share of of the US plasma donation center are located on the southern border near Mexico. In 2021, a new federal policy stopped permitting Mexican citizens from coming into the US on tourist visas to sell blood plasmas. In this project, you will use data to explore how the new policy affects the supply of blood products in the US. by Prof. Qian Zhao

I have two possible projects. The first is about the estimation of current COVID-19 daily infection using wastewater data and machine learning tools. This work is based on the result of 2022 REU. We plan to add wastewater data to the training set and re-train the neural network, so that the COVID-19 daily infection count can be more accurately estimated. If time permits, we will build a website showing the current COVID-19 daily infection in each state of the US. The second project is about investigating the valley structure of high dimensional landscape. Students must have some basic knowledge of stochastic differential equations in order to proceed. I list it here just in case some advanced undergraduate students are interested in it. by Prof. Yao Li

This project focuses on reducing the dimensionality of an ODE system that originates from quantum mechanics. No quantum mechanics knowledge required. by Prof. Weiqi Chu

Knot theory and Heegaard Floer homology: Two seemingly different knots may actually be the same (by dragging it around and looking at it from a different angle). So we come up with algebraic invariants to tell them apart and Heegaard floer homology is one of them, which can be computed combinatorially. This project aims to introduce Heegaard floer homology for knots and how to effectively compute it. by Prof. Jie Min

Mathematics of generative modeling; algorithmic aspects of generative modeling; Sampling methods for Bayesian inference; by Prof. Benjamin Zhang

Mathematical and computational models related to cell motility and the collective behaviour of cells in a tissue by Prof. Andreas Buttenschoen

Variance Reduction Techniques in Statistical Physics -- Many physical properties of materials are computed through statistical sampling of large numbers of microscopic configurations. The sampling error is typically the limiting factor in the accuracy of such methods. The project will build skills in computing, numerical analysis, and math modeling of physical systems by Prof. Matthew Dobson

Optimal Control of Nonlinear Waves for Atomic and Optical Physics Applications by Prof. Panos Kevrekidis.

Wave shape analysis for non-stationary time series using time-frequency analysis: we will analyze the oscillatory patterns of a non-stationary time series with the help of time-frequency analysis (among which, the Fourier transform is the simplest one). The application of these analytical approaches will be demonstrated in the context of medical signal analysis by Ziyu Chen.

A study of the Lambert (or log product) function.This is a not so well-known function with diverse applications to several areas, from medicine and biology, to chemical engineering, to statistics, mathematics, cosmology and black hole physics by Floyd Williams.

Solving inverse problems through Bayesian perspective by FNU Pranjal.

1. The Turnaway Study (https://www.ansirh.org/research/ongoing/turnaway-study) tried to determine the effect of being denied a wanted abortion by examining pregnant people who were just below the gestational age cutoff for their state (and thus received an abortion) and those who were just above (and thus did not receive an abortion). This project will explore the statistics underlying this design. 2. Black men who have sex with men (MSM) are more likely to be HIV+ than white MSM, even though they have higher rates of condom usage, testing, and other protective behaviors. This project will explore how segregation could explain this phenomenon. 3. The minimum spanning tree (MST) of a graph is a subset of the edges that contains no cycles, connects all vertices, and has the minimum total edge weight of all spanning trees. This project will explore what can be inferred about the MST of a population graph from the MST of a sample graph. 4. I’m also curious about the statistical methods used in the study of voting rights, perhaps starting with the work of the MGGG Redistricting Lab (https://mggg.org/). by Prof. Jonathan Larson.

images created using DALL-E 2