This will be an introductory talk on the theory of random polynomials and random matrices for the visiting graduate students. We will give a broad overview of the fields as well as some of the research directions being pursued in this department.

Overview of Random Polynomials and Random Matrices

Tue, Mar. 5 10:10am (MATH …

Geometry/Analysis

Ian Miller (CU Boulder)

X

The magnetic nonlinear Schrödinger (mNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In mNLS, identities involving motion are less well-behaved and cause difficulty for establishing blow-up results. Blow-up results have been obtained for mNLS with constant magnetic field. These results relied on the specific structure and symmetry of these potentials. In this talk we establish existence of blow-up solutions for a class of potentials with no prescribed symmetry.

Blow-up results for the nonlinear Schrödinger equations with trapping magnetic potentials

Tue, Mar. 5 2:30pm (MATH 3…

Lie Theory

Florencia Orosz Hunziker (University of Colorado Boulder)

X

Modular forms played an important role in the proof (Borcherds 1992) of the Monstrous Moonshine conjecture providing the first fundamental bridge between number theory and representation theory through vertex algebras. In this talk, we will give an overview of several ways in which Vertex algebras can be systematically be used to connect representation theory to number theory.

Connections between Representation Theory and Number Theory through vertex algebras

Tue, Mar. 5 3:30pm (MATH 3…

Topology

Alexander LaJeunesse

X

In this talk I will introduce monads and their algebras. Following a discussion of the relationship between monads and adjunctions, we will discover how every operad gives rise to a monad, and with this in hand we will spend some time trying to understand May’s comparison theorem. If time permits, we will conclude by looking at how the monadic bar construction can be used to construct canonical resolutions of algebraic objects.