Title: URA Presentations
| Speakers: | Tom Iagovet, Joseph Vendryes, Jacob Mausberg, Yun Xing |
| Affiliation: | University of Waterloo |
| Location: | MC 5479 |
Abstract: A series of presentations by a group of Spring 2023 Undergraduate Research Assistants. The topics of each presentation are detailed below.
Mathematical proof formalization - Tom Iagovet
Mathematical proof formalisation refers to the process of writing proofs in a way that is intended to be verified by a computer rather than a human. In this talk, we show what proof formalisation looks like in practice with examples from the lean-matroids library for the proof assistant Lean.
Counting $d$-regular graphs excluding an edge set - Joseph Vendryes
In this talk we will discuss a method for approximating the number of $d$-regular graphs on $n$ vertices, and we will consider how to modify this method to count how many $d$-regular graphs on $n$ vertices share no edges with a given graph $X$. Based on work by N. Wormald and A. Liebenau.
Evolution of random representable matroids - Jacob Mausberg
I will talk about my research with Jane Gao and Peter Nelson on random representable matroids. For a random n by m matrix A over F_q, we investigate the evolution of M[A], the random matroid represented by A, as m grows. Building on the work of Kelly and Oxley, we study the first appearance of certain classes of minors, circuits of given lengths, as well as the first time that M[A] becomes k-connected.
Tournaments and tournament stable sets - Yun Xing
A tournament G is an orientation of a complete graph. A stable set is a set of vertices X such that the induced subgraph G[X] is acyclic. Finding a maximum stable set in a tournament is an NP-complete problem. However, if there is a forbidden induced subgraph H for G, the problem might be solved in polynomial time. In this talk, we give our results on possible forbidden structures H.