Directed Reading Program at the University of Illinois Chicago

Using Causal Inference To Study the Spread of COVID-19
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We demonstrate a use case of causal inference to learning a Bayesian network modeling the spread of COVID-19 across the USA. We describe the methods used as well as challenges faced. We also interpret the model learned and discuss additional methods to potentially improve its accuracy.

Sheaves and Cohomology: An Introduction
Max Nguyen, mentored by Vignesh Jagathese
Abstract: This presentation will introduce the notion of a sheaf, a useful tool to study properties of spaces. Despite this, sheaves still have some shortcomings. By studying these shortcomings one can derive a powerful invariant in the form of cohomology.

Convergence Theorem for Finite Markov Chains
Sebastian Tous, mentored by Nick Christo
Abstract: When does a finite Markov chain converge? At what rate does convergence occur? In this presentation, I will discuss the prerequisite conditions for convergence and give a full proof of the Convergence Theorem for Finite Markov Chains.

Representations and Lie Groups
Mustafa Nawaz, mentored by Jennifer Vaccaro
Abstract: In this talk, we will define Lie groups, Lie algebras, and representations. We will discuss properties, and present Schur’s Lemma.

The Mathematics of Pricing Assets
Raghav Bhutani, mentored by Kevin Zhou
Abstract: This presentation introduces essential financial tools, focusing specifically on derivatives. We will explore the fundamental mechanics of derivatives, including detailed visual representations through payoff diagrams. The core of the discussion will center on the pricing of these assets, particularly through the lens of the Black-Scholes formula. Attendees will gain an understanding of what the Black-Scholes formula represents, its significance in financial markets, and its practical applications in asset pricing.

Introduction to Ideals and Varieties
Emma Todd, mentored by Emily Cairncross
Abstract: The discussion will define and cover some examples of affine varieties. Then we will define general ideals and radical ideals and explore their connection to varieties.

Models of Random Graphs
Juan Jose Rosendo, mentored by Katie Kruzan
Abstract: There are various models of random graphs that have different purposes. The different models and the Preferential Attachment Model. Each model will be defined, accompanied with an that will be introduced are the Erdos-Renyi graph, Generalized Random Graphs, Configuration Model, example. Last, a brief description behind the motivation of each model will be given.

Foundations of of Machine Learning: Learning Guarantees and Dimensionality Reduction
Markus Perez, mentored by Duan Tu
Abstract: When designing machine learning systems, fundamental questions from “What can be learned?” to “Can we design accurate and efficient learning algorithms?” arise. This presentation will provide an introduction to the PAC-Learning Framework, which allows us to analyze learnability, and the related concepts of Rademacher Complexity and VC-Dimension. Additionally, the basics of Dimensionality Reduction will be covered.