# Events for 02/22/2019 from all calendars

## Combinatorial Algebraic Geometry

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

**Location:** Bloc 506AX

**Speaker:** Frank Sottile, Texas A&M University

**Title:** *Numerical computation of multiprojective varieties*

**Abstract:** A multiprojective variety is a subvariety of a product of projective spaces. They may be studied as projective varieties under the Segre embedding or locally as affine varieties in an affine patch. Both approaches have disadvantages, increasing complexity or ignoring structure. I will discuss methods from numerical algebraic geometry to study multiprojective varieties that take advantage of their structure and do not increase the complexity of the numerical representation. This is joint work with Hauenstein, Leykin, and Rodriguez.

## Probability Seminar

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

**Location:** BLOC 628

**Speaker:** Alex Hening, Tufts University

**Title:** *Stochastic persistence and extinction*

**Abstract:** A key question in population biology is understanding the conditions under which the species from an ecosystem persist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we look at the competitive exclusion principle from ecology and show how the random switching can `rescue' species from extinction. The talk is based on joint work with Dang H. Nguyen (University of Alabama).

## Banach Spaces Seminar

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

**Location:** BLOC 220

**Speaker:** Alexandros Ezkenasis, Princeton University

**Title:** *Progress on Enflo's conjecture*

**Abstract:** In modern terminology, Enflo's conjecture (1978) asserts that a Banach space X has Rademacher type p if and only if it satisfies a metric property called Enflo type p. Loosely speaking, the conjecture suggests that all X-valued functions on the Hamming cube satisfy a dimension independent L_{p} Poincare inequality if and only if the same inequality is satisfied merely for linear functions. In his 1986 work, Pisier showed that Banach spaces of Rademacher type p have Enflo type q for every q

## Algebra and Combinatorics Seminar

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

**Location:** BLOC 628

**Speaker:** Westin King, TAMU

**Title:** *Decompositions of Parking Functions on Trees*

**Abstract:** Parking functions describe a sequence of drivers attempting to find a place to park in a one-way linear parking lot. We can introduce a more complicated "parking lot" by considering directed trees and again ask if all the drivers can park. In this talk, I will give enumerative results concerning certain types of these generalized parking functions by considering decompositions based on the movement of drivers while they attempt to park. Additionally, I will discuss the number of "lucky drivers," those who park in the first parking space they encounter, and will find they are related to the Narayana numbers, which refine the ubiquitous Catalan numbers.

## Student Working Seminar in Groups and Dynamics

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

**Location:** BLOC 624

**Speaker:** Amanda Hoisington

**Title:** *Intro/Overview to Baum-Connes Conjecture*

## Linear Analysis Seminar

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

**Location:** BLOC 220

**Speaker:** Corey Jones, Ohio State University

**Title:** *Generalized crossed products and discrete subfactors*

**Abstract:** We will describe a generalization of the crossed product construction for von Neumann algebras, where a group action on the algebra is replaced by a rigid C*-tensor category action on the algebra, together with a W*-algebra object internal to this category. Every spherical discrete extension of a II1 factor can be uniquely realized as such a crossed product. We will discuss some examples and applications. Based on joint work with David Penneys.