The Chromatic Index of 3-Uniform 3-Partite Random Hypergraphs

Mason Shurman 

December 1st, 2025 (Monday) at 3pm - NSII 1201

Abstract

The \textit{chromatic index} of a graph, denoted \(\chi'(G)\), is the minimum number of colors required to color its edges such that no two edges of the same color share a vertex. Vizing's theorem, a classical result in graph theory, states that the chromatic index of a graph is either $\Delta(G)$ or $\Delta(G)+1$, where $\Delta(G)$ is the maximum number of edges that lie on any vertex.  It is natural to extend the notion of chromatic index to hypergraphs, where edges may contain more than two vertices. For hypergraphs, Vizing's theorem does not always hold: it is possible to construct examples with much larger chromatic index than the maximum degree. We show that this is not usually the case: for the random hypergraph $H \sim H^3_{n,1/2}$, with $n$ vertices where each possible $3$-edge is included with probability $1/2$, with high probability $\chi'(H)=\Delta(H)$. For the sake of brevity and clarity, this talk will mostly focus on a slightly simpler case: random $3$-partite $3$-uniform hypergraphs, where we also show that the chromatic index equals the maximum degree. This work is joint with Asaf Ferber, Marcelo Sales, and Arnab Chaterjee.

About the Speaker

Mason Shurman is a 4th year PhD student studying under Asaf Ferber. His research interests include random graphs, combinatorial games, and other areas of discrete math. In his free time, Mason loves to play piano and go rock climbing.  

Anderson Localization: From Spectral Theory to Quantum Dynamics 

Omar Hurtado 

June 2nd, 2025 (Monday) at 1pm - NSII 1201

Abstract

Anderson localization is a phenomenon first posited by physicist P. Anderson in Nobel prize winning work, where disorder in a material frustrates electronic transport, thus "localizing" wave functions (forcing them to remain more or less constrained to a small area forever even under the system's time evolution). Decades later, this phenomenon has been proven, empirically and theoretically, to a large degree. We recall the basics of spectral theory for Hilbert spaces, and basic quantum mechanical background before discussing the relationship between the spectral theory of a Hamiltonian and the associated dynamics in the context of Anderson localization. We will discuss the history of mathematically rigorous results concerning Anderson localization, and some of the key techniques. Time permitting, the speaker will discuss some of their own work in this field and key ideas therein.

About the Speaker

Omar Hurtado is a 6th year PhD student of Svetlana Jitomirskaya interested in the intersection of mathematical physics, spectral theory and probability.

The Unreasonable Effectiveness of Linear Models In Time Series Forecasting

Elisha Dayag

March 14th, 2025 (Friday) at 3pm - RH 510R

Abstract

Can we predict future traffic, energy usage, or stock prices using historical data? While deep learning, particularly Transformer-based methods, has excelled in areas like computer vision and natural language processing, it has been found to underperform compared to simpler linear models in time series forecasting. This talk discusses recent hypotheses explaining why linear models remain competitive and presents empirical evidence supporting and challenging these ideas. Based on joint work with Nigus Teklehaymanot and Nhat Thanh Van Tran.

About the Speaker

Elisha Dayag is a fourth year graduate student working with Jack Xin who is interested in all applications of deep learning, but especially computer vision and scientific machine learning.