The Fall 2023 DRP at UIC Presentation Session was held on December 1, 2023. There were four presentations:
Towards counting lines on a smooth cubic
Leila Dahlia, mentored by Sixuan Lou
Abstract: We will introduce modern machinery to count
numbers of lines lying on a given surface.
Algebraic Topology and The Fundamental Theorem of Algebra
Mustafa Nawaz, mentored by Michael Gintz
Abstract: We will talk about the notion of homology and how it can be used to give an invariant of a circle. Then, using this we can prove the fundamental theorem of algebra.
Markov Chains: Introduction and Applications
Zahra Vasi, mentored by Clay Mizgerd
Abstract: Markov chains serve as useful mathematical models for studying movements among elements in a set. These chains have unique properties that allow mathematicians to understand and predict their long-term behavior. This presentation discusses some essential definitions and properties associated with Markov chains and several examples of useful and interesting applications.
Computational Learning Theory and Probabilistic Models
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We examine the framework of PAC learning and provide examples of problems that are PAC learnable as well problems that are not. We then investigate this framework applied to learning Bayesian Networks. We address the limitations of this framework, and provide a concrete example of learning a Bayesian network given real-world medical data.