Presentations are in two sessions: Wednesday, April 29, 2025 from 12:00-1:00pm and Thursday, April 30 from 1:00-3:00pm in SEO 636!
(mentored by Abhijeet Mulgund)
This presentation explains how model specification (our choice of variables and model) can lead to different conclusions from the same data. This is related to concepts such as identifiability, the bias–variance tradeoff, and the distinction between prediction and inference.
(mentored by Darius Alizadeh)
I'm going to go over what a loop is, what it means for two loops to be equivalent, and give a general idea of what the fundamental group is on R^2 and the circle. If there's time I will give more examples of the fundamental group on different spaces.
(mentored by Andre de Moura)
I will go over what a representation is and some tools we can use to study them, with some examples.
(mentored by Nick Christo)
The probabilistic method can be used to prove that something exists without explicitly constructing it. In this presentation, we will introduce some basic graph definitions and the Ramsey number, and then we will use the so-called probabilistic method to prove a lower bound on the Ramsey number R(K_k,K_k).
(mentored by Lisa Cenek)
In my presentation I will give an overview on what graph theory is and its real world application. Then I will discuss a lemma on trees and also a theorem on trees.a
(mentored by Theo Sandstrom)
We will introduce the basics of type theory and the Curry--Howard isomorphism.
(mentored by Anh Tran)
I will present a nice problem related to the Lie group SO(3,R) and a "baby version" of this problem. I will also present the answer to the baby version, but only briefly discuss the answer of the original problem.
(mentored by Dane Meade)
I'm going to use the definition of Lipschitz continuity to show that the distance function is continuous and uniformly continuous. Additionally, I'm going to show that the Takagi function which is related to the distance function is continuous everywhere, but nowhere differentiable.
(mentored by Xiaoning Shi)
This presentation introduces discrete-time Markov chains and their long-term behavior, including transition matrices, state classification, and stationary distributions. It then applies these concepts to an M/M/1 queue, illustrating how key performance measures such as stability, queue length, and waiting time can guide practical decisions through parameter changes and cost analysis.