# Events for October 20, 2017 from General and Seminar calendars

## Postdoc Lunch Time Talks

**Time:** 12:00PM - 12:20PM

**Location:** BLOC 220

**Speaker:** Benben Liao, Texas A&M University

**Description:**Title: Group actions and non-commutative ergodic Theorems

Abstract: Starting from the work of Birkhoff, ergodic theory is one of the central themes in dynamical system. In this talk, we give a review of generalizations of ergodic Theorems with group actions and non-commutative measure spaces (von Neumann algebras), and show an ergodic theorem for groups with polynomial growth acting on von Neumann algebras. This is based on joint work with G. Hong and S. Wang.

## Postdoc Lunch Time Talks

**Time:** 12:35PM - 12:55PM

**Location:** BLOC 220

**Speaker:** Rob Rahm, Texas A&M University

**Description:**Title: A Dyadic Version of The Hilbert Transform and Other Operators.

Abstract: Consider the Hilbert transform (convolution with 1/x). For which measures is this operator bounded on L^2(\mu) and what is its norm in terms of "geometric" properties of the measure? We use a dyadic approximation to this (and other) operators to prove the desired estimates.

## Postdoc Lunch Time Talks

**Time:** 12:55PM - 1:15PM

**Location:** BLOC 220

**Speaker:** Emanuele Ventura, Texas A&M University

**Description:**Title: Waring and tensor ranks

Abstract: The problem of expressing a homogeneous polynomial as a sum of powers of linear forms is very classical and goes back to the work of Sylvester, Hilbert, Scorza and many others. The rank of a homogeneous polynomial is the smallest number of linear forms such that the polynomial admits such a representation. The tensor rank is the analogous notion for tensors. In this talk, we will introduce these notions through examples and describe directions of current research.

## Mathematical Physics and Harmonic Analysis Seminar

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

**Location:** BLOC 628

**Speaker:** Wen Feng, University of Kansas

**Title:** *Stability of Vortex solitons for n-dimensional focusing NLS*

**URL:** *Link*

## Algebra and Combinatorics Seminar

**Time:** 3:00PM - 3:50PM

**Location:** BLOC 117

**Speaker:** Benjamin SchrÃ¶ter, TU-Berlin

**Title:** *Multi-splits in hypersimplicies and split matroids*

**Abstract:**Multi-splits are a class of coarsest regular subdivisions of convex polytopes. In this talk I will present a characterization of all multi-splits of two types of polytopes, namely products of simplices and hypersimplices. It turns out that the multi-splits of these polytopes are in correspondence with one another and matroid theory is the key in their analysis, as all cells in a multi-split of a hypersimplex are matroid polytopes. Conversely, the simplest case of multi-splits of hypersimplices give rise to a new class of matroids, which we call split matroids. The structural properties of split matroids can be exploited to obtain new results in tropical geometry.

## Geometry Seminar

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

**Location:** BLOC 628

**Speaker:** Michael Di Pasquale, Oklahoma State University

**Title:** *Homological Obstructions to Freeness of Multi-arrangements*

**Abstract:**

If the module of vector fields tangent to a multi-arrangement is free over the underlying polynomial ring, we say that the multi-arrangement is free. It is of particular interest in the theory of hyperplane arrangements to investigate the relation of freeness to the combinatorics of the intersection lattice - the holy grail here is Terao's conjecture that freeness of arrangements is detectable from the intersection lattice. It is known that corresponding statements for multi-arrangements fail.

Given a multi-arrangement, we present a co-chain complex derived from work of Brandt and Terao on k-formality whose exactness encodes freeness of the multi-arrangement. The cohomology groups of this co-chain complex thus present obstructions to freeness of multi-arrangements. Using this criterion we give an example showing that the property of being totally non-free is not detectable from the intersection lattice. This builds on previous work with Francisco, Schweig, Mermin, and Wakefield.