Department of

Mathematics


Seminar Calendar
for Graduate Student Colloquium events the year of Tuesday, March 26, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, January 30, 2019

4:00 pm in 245 Altgeld Hall,Wednesday, January 30, 2019

Rescheduled

Wednesday, February 6, 2019

4:00 pm in 245 Altgeld Hall,Wednesday, February 6, 2019

Systems of Calogero-Moser Type

Matej Penciak (Illinois Math)

Abstract: It is well known that many-particle systems are in general not solvable analytically. For some specific choices of interactions between particles though, a lot can be said. In this talk I aim to give an introduction to systems of Calogero-Moser type and the surprising role of algebraic geometry in their solvability. I will also give a perspective on how this subject plays a role in some hot topics in mathematics in general: Hitchin integrable systems, geometric representation theory, and the geometric Langlands philosophy.

Wednesday, February 20, 2019

4:00 pm in 343 Altgeld Hall,Wednesday, February 20, 2019

Connecting Boolean (un)satisfiability to Graph Theory

Vaibhav Karve (Illinois Math)

Abstract: Given a Boolean formula can we find consistent assignments (True or False)for variables such that the formula is satisfied? This is the Boolean Satisfiability problem, a problem of great historic value in computer science. It is the first problem that was proven to be NP-complete. In this talk, I will introduce Satisfiability and explain what the terms P, NP, NP-complete... mean. I will then demonstrate a (surprising)connection between Boolean formulas and graph theory which will help us gain a more visual understanding of when a class of formulas is satisfiable or unsatisfiable. There will be lots of small graphs in this talk.

Monday, March 11, 2019

2:00 pm in 245 Altgeld Hall,Monday, March 11, 2019

A brief survey of extremal combinatorics and some new results for (hyper)graphs

Ruth Luo (Illinois Math)

Abstract: Extremal combinatorics is a branch of discrete mathematics which studies how big or how small a structure (e.g., a graph, a set of integers, a family of sets) can be given that it satisfies some set of constraints. Extremal combinatorics has many applications in fields such as number theory, discrete geometry, and computer science. Furthermore, methods in extremal combinatorics often borrow tools from other fields such as algebra, probability theory, and analysis. In this talk, we will discuss some benchmark results in the field as well as some recent results for extremal problems in graphs and hypergraphs.

Wednesday, April 17, 2019

4:00 pm in 245 Altgeld Hall,Wednesday, April 17, 2019

From Graph Laplacian to the Stability of Coupled Oscillator Networks

Lan Wang (Illinois Math)

Abstract: There is a large amount of applied problems that can be posed as dynamical systems on a coupled oscillator network. Frequently these problems involve computing the inertia of a graph Laplacian. In this talk we will start with an overview of the properties of the Laplacian matrix and then explore how it functions in the study of the stability of fixed points of dynamical systems. Particularly, we will discuss the Kuramoto model, a classic and popular model for describing the dynamics of a large population of coupled oscillators. We will first deliberate the stability of the phase-locked solutions of Kuramoto model on single-layer networks, and then extend it to multi-layer networks by examining the Supra-Laplacian matrix.