Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015 Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015 Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015 Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015 Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015 Graduate Student Seminar, Department of Mathematics, University of Notre Dame, 2014-2015

Notre Dame Math Graduate Student Seminar, 2014-2015

The Graduate Student Seminar is put on by the Mathematics Graduate Student Association . GSS meets approximately every other Monday.

For the Fall 2014 semester, the GSS meets at 4:00p in 125 HH.

Previous Semesters

To volunteer to give a talk, or for anything else regarding the seminar, contact Dominic Culver.

Schedule Fall 2014

Date Speaker Title
Monday, September 8 Katrina Barron An Introduction to the Algebraic Aspects of Conformal Field Theory and Applications
Monday, September 22 Augusto Stoffel 2-Dimensional Topological Field Theories
Monday, Octobr 6 Edward Burkard A Primer on Pseudoholomorpic Curves

Schedule Spring 2015

Date Speaker Title

Abstracts

September 8, 2014

Speaker
Katrina Barron
Title
An Introduction to the Algebraic Aspects of Conformal Field Theory and Applications
Abstract

Conformal Field Theory (CFT) is an attempt to unify all fundamental forces, including gravity, by modeling particles as vibrating strings. In the genus-zero, two-dimensional setting, vertex operator algebras (VOAs) describe the particle interactions. Independently from physics, VOAs were discovered in mathematics in the study of representations of infinite-dimensional Lie algebras and the Monster finite simple group. This study led to the surprising connection between CFT, VOAs and number theory. I will briefly give a flavor of some of the mathematics involved.

September 22, 2014

Speaker
Augusto Stoffel
Title
2-Dimensional Topological Field Theories
Abstract

We will show that the notion of a topological field theory, in one of its simplest variations (namely, 2-dimensional and oriented), recovers a classical notion from algebra, that of a Frobenius algebra. This fact is a well-known “folk theorem” but, as we will see, it has a nontrivial proof relying on Morse theory.

October 6, 2014

Speaker
Edward Burkard
Title
A Primer on Pseudoholomorpic Curves
Abstract

I will begin with an overview of almost complex manifolds and complex manifolds. Next, I will define pseudoholomorphic curves (or (J-)holomorpic curves) and I will try to convince you that these are just the usual notion of a holomorphic function in a special case. After that, I will give some basic definitions in symplectic geometry and relations with almost complex structures. Finally, I will state some results in symplectic geometry which are applications of holomorphic curves, one of which can be thought of as a generalization of the Riemann Mapping Theorem.


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