Fall 2018

The seminar has concluded. Thanks to all the speakers and attendees for making this seminar great!

Dec. 6, 2018

Speaker: Parker Hund

Title: An introduction to Lie and representation theory in physics

Abstract: Since I am not quite ready to talk about stars, instead I will talk about some things in a very different direction. I will talk about the relations among and representations of the groups and corresponding algebras of U(1), U(2), SU(2), and SO(3). I will also talk about the Schrodinger representation of the Heisenberg group and algebra. All of the physics necessary to understand the applications will be explained in the talk.

Nov. 22, 2018

Happy Thanksgiving!

Oct. 31, 2018

Wednesday

Time: 12:15 - 1:15PM

Joint with the Graduate Combinatorics Seminar:

Speaker: Bhargav Narayanan

Title: Cutting Cake with Algebraic Topology

Abstract: A group of people want to divvy up a piece of cake "fairly". What does "fairly" mean? How do they this? What does this have to do with the Borsuk--Ulam theorem? I will try to say something about these questions, and a bit more, time permitting.

Speaker: Vladimir Retakh

Title: Introduction to Noncommutative Birational Geometry

Abstract: I will discuss several phenomena related to noncommutative triangulations of surfaces.

Oct. 25, 2018

Speaker: Yi-Zhi Huang

Title: Mathematical two-dimensional conformal field theory

Abstract: Quantum field theory has become an active research
area in mathematics in the last forty years. Two-dimensional
conformal field theory as a best understood nontopological
quantum field theory has been greatly developed and
has also directly provided ideas and methods for the successful
solutions of mathematical conjectures and problems. But many
deep and important mathematical problems are still open. In this talk,
I will give an introduction to the mathematical study of
two-dimensional conformal field theory and discuss some
open problems as presented in my paper:

Y.-Z. Huang, *Some open problems in mathematical two-dimensional
conformal field theory*, in: Proceedings of the Conference on Lie Algebras,
Vertex Operator Algebras, and Related Topics, Contemp. Math, Vol. 695,
American Mathematical Society, Providence, RI, 2017, 123--138.
arXiv:1606.04493

Oct. 18, 2018

Speaker: Sven Moeller

Title: Generalised Deep Holes and the Genus of the Moonshine Module

Abstract: Conway, Parker and Sloane observed that the deep holes of the Leech lattice are in natural bijection to the other 23 Niemeier lattices. I will explain this miraculous observation and mention a similar result for holomorphic vertex operator algebras I recently discovered.

Oct. 11, 2018

Speaker: Terence Coelho

Title: From Lattices to Lie Algebras

Abstract: We show how to construct simple Lie algebras of type A,D, or E from its corresponding lattice. These lattices are often easy to define and provide a natural basis for the algebra.

Oct. 4, 2018

Speaker: Alejandro Ginory

Title: Representation Theory of Finite Groups

Abstract: We give an introduction to the representation theory of finite groups with a special emphasis on motivation. Much of the concepts generalize to compact groups as well. We then present the representation theory of the symmetric group and illustrate the beautiful combinatorics used to characterize it. The latter part will feature partitions, Young tableaux, and character tables!

Sept. 27, 2018

Speaker: Jason Saied

Title: Root Systems

Abstract: This talk will assume no knowledge of Lie algebras or representation theory, not even from last week’s talk! I will start by explaining and giving examples of some basic notions. I will then go through the (very simple and nice) representation theory of a particularly important three-dimensional Lie algebra, sl_2, in detail. After this, I will define the root system of a semisimple Lie algebra and use what we know about sl_2 to derive some of its basic properties. (Skipping anything that’s too technical, but showing some of the nicer arguments.) I will then try to explain how understanding root systems leads to a classification of semisimple Lie algebras. If we have extra time, I will discuss the generalization to Kac-Moody algebras and their root systems.

Sept. 20, 2018

Speaker: Songhao Zhu

Title: A Brief Introduction to the Representation Theory of Lie Algebras

Abstract: Lie algebras are one of the central subjects studied in representation theory. Why do we care about them in the first place? What do we mean by 'we care'? In specific, concepts and theorems on structures, classification of semisimple Lie algebras, and their modules, will be presented. Classical examples with various applications in other fields will be discussed, as well as for the purpose of supporting the concepts introduced. Poor illustrations will possibly be drawn on the blackboard with very poor skills in contrast to the beautiful ideas behind them.