Graduate student colloquium
Graduate student colloquium
Spearheaded by myself, and co-organized with Ivan So, the graduate student colloquium was a venue in which graduate student mathematicans at MSU presented their research or gave expository talks to other grad students, in general-audience style talks.
As of May 2024, the graduate student colloquium is concluded for the F23-S24 academic year. It may return next year, but who knows! You can find all the speakers and abstracts below.
---- 04/02/2024 ----
Speaker: Aldo Garcia Guinto, MSU
Title: Free Probability Theory
When: Tuesday, April 2, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: In this talk, we shall introduce the notion of freeness, defined by Voiculescu, for unital algebras with an unital linear functional. The notion of freeness comes from that of groups. Given a group, one can define a unital linear functional on the group algebra and this linear functional can detect if our group comes from the free product of its subgroups. This in turn will allow us to define when unital subalgebras and elements of our algebra are free.
---- 03/19/2024 ----
Speaker: Eloy Moreno-Nadales, MSU
Title: Quantum Trajectories
When: Tuesday, March 19, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: Beginning with the basics of quantum mechanics, we speak about quantum systems and how they evolve. We discuss quantum trajectories and the work of purification in an article from Kümmerer and Maassen in 2006. We now add noise and disorder. We comment on a generalization of quantum trajectories to a noisy environment. Group project with O. Ekblad, L. Pathirana, J. Schenker and myself. Soon on arXiv.
---- 02/20/2024 ----
Speaker: Peikai Qi, MSU
Title: Knots and Primes
When: Tuesday, February 20, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: We will first talk about the analogy between the circle S^1 and the finite field Fp. Then we introduce some of the analog between knot S^1 embedding in R^3 and Spec(Fp) embedding in Spec(Z). If time allows, we will talk about the analogy between link number and Legendre symbol in detail. Finally, we will briefly discuss about the striking analogy between the infinite cyclic cover and Iwasawa theory.
---- 02/06/2024 ----
Speaker: Owen Ekblad, MSU
Title: Information Theory, from Classical to Quantum
When: Tuesday, February 6, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: What does it mean to communicate? One possible intuitive answer is that communication is the exchange of information. Implicit in this answer is the following question: what do we mean by “information”? In this talk, I will discuss the perspective that information is an intrinsically physical concept, so that, in particular, different theories of physics give rise to different theories of information. With this in mind, I will introduce the rudiments of quantum mechanics, bringing us to the basic mathematical theory of quantum information. This talk is self-contained and assumes no prior knowledge of physics or information theory.
---- 01/23/2024 ----
Speaker: Jie Yang, MSU
Title: An Elementary Introduction to the Langlands Program
When: Tuesday, January 23, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: The Langlands program is now an important and fascinating area in number theory. In this talk, I aim to explain why we care about the Langlands program and what it is. The talk is intended for the general audience.
---- 11/21/2023 ----
Speaker: Ivan So, MSU
Title: The Wildworld of Manifolds of Dimension 3 and 4
When: Tuesday, November 21, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: In this talk, I will talk about Kirby calculus, a major tool in low dimensional topology, in both dimension 3 and 4 and how the two are related. Not all low-dimensional topologists are knot theorists, but hopefully after this talk you will see why topologists will need some understanding of knots and links.
---- 10/17/2023 ----
Speaker: Keshav Sutrave, MSU
Title: Particle Physics: Gauge theory and a Higgs Mechanism
When: Tuesday, October 17, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: Physics has come a long way from the simple models we used in Newton’s era. Instead of acceleration and force vectors, we work with with "principal bundles" and "gauge fields". I’ll introduce a little bit of this “gauge theory" setup which we use to model interactions in modern particles physics, along with an example of a Higgs mechanism, in which adding a particle allows us to explain why some particular particles (which should have been massless) do in fact have mass.
---- 10/10/2023 ----
Speaker: Jamie Kimble, MSU
Title: Tangled Labelings of Partially Ordered Sets
When: Tuesday, October 10, 4:30pm-5:20pm (note the unusual time)
Where: Wells Hall C304
Abstract: This expository talk will give background on posets, promotion, and tangled labelings before describing our latest conjectures. Promotion is a cyclic group action on the linear extensions of a poset; it has numerous connections to algebraic combinatorics, representation theory, and sorting algorithms. In 2022, Colin Defant and Noah Kravitz introduced promotion sorting, an operator on poset labelings that generalizes promotion. In their paper, they demonstrate that any labeling of an n-element poset will map to a linear extension of it after at most n − 1 applications of the promotion sort operator. Labelings that require exactly n−1 applications are called tangled labelings, since they are the furthest from being sorted. They enumerate the number of tangled labelings for certain special classes of posets. They conjecture (n − 1)! as an upper bound for the number of tangled labelings of any n-element poset. We have determined a new conjecture for this upper bound. Based on ongoing work with Margaret Bayer, Herman Chau, Mark Denker, Owen Goff, Joel Jeffries, Lauren Kimpel, Yi-Lin Lee, Jinting Liang, and Nick Veldt.
---- 09/26/2023 ----
Speaker: Ivan So, MSU
Title: How gauge theories play a role in topology
When: Tuesday, September 26, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: Gauge theory is an old concept that originated from physics. Important physical theories as classic as the Maxwell's equations, as modern as quantum chromodynamics are all gauge theories in different flavor. Starting from the 1970s, mathematicians began to study them for geometric purposes. In the 1980s, there was an utterly unexpected development in topology owing to gauge theory. In this talk, I will illustrate what gauge theories are from the Maxwell's equations and of course, the developments in topology owing to gauge theory.
---- 09/12/2023 ----
Speaker: Minh Le, MSU
Title: Blow-up prevention for some Chemotaxis models
When: Tuesday, September 12, 4:10pm-5:00pm
Where: Wells Hall C304
Abstract: The focus of this talk is on solutions to a two-dimensional Keller-Segel system containing sub-logistic sources. We show that the presence of sub-logistic terms is adequate to prevent blow-up phenomena even in strongly degenerate Keller-Segel systems. Our proof relies on several techniques, including parabolic regularity theory in Orlicz spaces, variational arguments, interpolation inequalities, and the Moser iteration method.