# Events for October 13, 2017 from General and Seminar calendars

## Several Complex Variables Seminar

**Time:** 11:00AM - 12:00PM

**Location:** BLOC 220

**Speaker:** Blake Boudreaux, TAMU

**Title:** *The Boundary Behavior of Biholomorphic Maps: An Example by B. L. Fridman*

**Abstract:**This expository talk follows a construction by B. L. Fridman of two bounded domains in C^2 that are biholomorphically equivalent to the unit bidisc (and hence each other), but no biholomorphism between the domains can extend continuously to the boundary. This shows that there is no straightforward generalization of the classical theorem of Carathéodory to higher dimensions.

## Number Theory Seminar

**Time:** 1:00PM - 2:00PM

**Location:** BLOC 605AX

**Speaker:** Dinesh Thakur, University of Rochester

**Title:** *Multizeta values and related structures in the function field setting*

**Abstract:**We will introduce multizeta and compare the number field situation with the function field situation.

**URL:** *Link*

## Promotion Talk - Marco Roque-Sol

**Time:** 1:00PM - 2:00PM

**Location:** BLOC 220

**Speaker:** Marco Roque-Sol, Texas A&M University

**Description:**

Title: An introduction to Solitons.

Abstract:

The study of differential equations plays an essential role in applying mathematics to physical systems. A mathematically important aspect of these studies is the theory of integrable systems, which currently plays an important role in many branches of modern mathematics and mathematical physics, among those we can find: Oscillations in Classical Mechanics, wave equation in Electrodynamics, Schrõdinger equation in Quantum Mechanics, ( Ernst ) Ising model to explain ferromagnetism in statistical mechanics, quantum field theory (QFT), a set of quantum mechanical models of subatomic particles, Solitons, ... etc. This presentation gives a survey of the soliton theory, starting by introducing some historical remarks, basic concepts of the mathematical aspects of Soliton Theory, and later on, talking about the KdV ( Diederik Korteweg and Gustav de Vrise) equation with its traveling wave solution. The aim of this talk is to serve as an introductory session to the more advanced material related to global attraction to solitary waves where we study properties of solitary wave solutions of the form φ(x)e^{-iωt} , with ω real and φ(x) localized in space.

## Mathematical Physics and Harmonic Analysis Seminar

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Dmitri Pelinovsky, McMaster University

**Title:** *Nonlinear Schrodinger equation on the periodic graph*

**Abstract:**With a multiple scaling expansion, an effective amplitude equation can be derived for an oscillating wave packet. Using Bloch wave analysis and energy methods, we estimate the distance between the macroscopic approximation which is obtained via the amplitude equation and true solutions of the NLS equation on the periodic metric graph. These approximations are discussed in the context of bifurcations of standing localized waves on the periodic metric graphs. This work is joint with Guido Schneider (Stuttgart).

## Algebra and Combinatorics Seminar

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 117

**Speaker:** Yiby Morales, Universidad de los Andes

**Title:** *The five-term exact sequence for Kac cohomology*

**Abstract:**The group of equivalence classes of abelian extensions of Hopf algebras associated to a matched pair of finite groups was described by Kac in the 60’s as the first cohomology group of a double complex, whose total cohomology is known as the Kac cohomology. Masuoka generalized this result and used it to compute some groups of abelian Hopf algebra extensions. Since Kac cohomology is defined as the total cohomology of a double complex, there is an associated spectral sequence. I will explain how we compute the five-term exact sequence associated to this double complex, which can be used to compute some other groups of abelian extensions. This is joint work with César Galindo.

## Linear Analysis Seminar

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Mehrdad Kalantar, University of Houston

**Title:** *Superrigidity relative to subgroups*

**Abstract:**We present several ergodic theoretical and operator algebraic superrigidity results for discrete groups relative to their subgroups. These results are obtained by analyzing the restriction of boundary actions to subgroups. This is joint work with Yair Hartman.

## Geometry Seminar

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 628

**Speaker:** Emre Sen, Northeastern

**Title:** *Singularities of dual varieties associated to exterior representations*

**Abstract:**For a given irreducible projective variety $X$, the closure of the set of all hyperplanes containing tangents to $X$ is the projectively dual variety $X^{\vee}$. We study the singular locus of projectively dual varieties of certain Segre-Pl\"{u}cker embeddings. We give a complete classification of the irreducible components of the singular locus of several representation classes. Basically, they admit two types of singularities: cusp type and node type which are degeneracies of a certain Hessian matrix, and the closure of the set of tangent planes having more than one critical point respectively. In particular, our results include a description of singularities of dual Grassmannian varieties.