Here is a list of past speakers at our graduate student seminar:
Speaker: Rachmiel “Rocky” Klein, Brandeis University
Title: “Geometric Group Theory: Visualizing groups and Curvature”
Abstract: Geometric group theory (GGT) is a field of math that has proven very useful in the past few decades. In addition to relating to ample other areas of pure mathematics it also relates to other subjects such as chemistry, art, and logic. But how is one to think about groups geometrically? In this talk I will lay out the foundations of GGT in three parts. In part one, which will take up a good portion of the lecture, I will explain how groups can be thought of geometrically by discussing large scale and coarse geometry. Part two will be about hyperbolic groups, and part three will consist of many examples for how negatively curved (hyperbolic) groups can help to solve many problems in abstract group theory. The goal of the lecture is to give the basics of the subject as opposed to proving a specific theorem. I will be happy to take questions along the way.
Info on the speaker: Rocky is a second year PhD student at Brandeis working with Dr. Carolyn Abbott in GGT.
Speaker: Vitor Emanuel Gulisz
Title: Functor categories and (higher) Auslander-Reiten theory
Abstract: In this expository talk, we will discuss how we can generalize rings to categories, so that we also generalize modules over rings to functors. As an application, we will see how such generalizations lead to the development of (higher) Auslander-Reiten theory. This talk is based on my master’s thesis: https://acervodigital.ufpr.br/handle/1884/71956
Speaker: Yujia Shi
Title: Quantum Walks and Perfect State Transfer
Abstract: Considering each particle of an n-qubit system as a vertex, we can describe quantum transport phenomena using graphs.
The probability of transferring the state of node u to node v at time t is given by p(t) = (u|e^(itH)|v)^2. Here the Hamiltonian, H, of this system corresponds to the adjacency matrix and energy potential. I will discuss the cases where perfect state transfer and strong state transfer happen.
Speaker: Sean Carroll
Title: Free subgroups of arithmetic groups
Abstract: Arithmetic groups, like SL2Z, are a central object of study in modern mathematics. In this talk I will give an introduction to arithmetic groups, and provide concrete examples from number theory, geometry, algebra, and topology.
We will then investigate the existence of free subgroups within a certain class of arithmetic groups.
Speaker: Ryan Kannanaikal
Title: Construction of Higher K Theory
Abstract: I will go through Quillen’s construction of higher K-theory, and go over some basic properties
Speaker: Dezhou Li
Title: Computing the configuration space of k unordered points over R^n using spectral sequences.
Abstract: Configuration spaces of manifolds are classical objects of study with connections to homotopy theory, geometric topology, algebraic geometry, and theoretical physics. (co)Homology of the configuration space of k ordered points over R^n has been well understood by Arnold and Cohen, but its unordered case over R^n is still worth studying. Schiessl computed the n=2 case using a cellular decomposition invented by Vainshtein. Since the action of symmetric group on the configuration space of k ordered points is free, we can acquire information about the unordered case using Cartan-Leray spectral sequence.