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# Events for 02/06/2019 from all calendars

## Geometry Seminar

## Groups and Dynamics Seminar

## AMUSE

**Time:** 2:00PM - 3:00PM

**Location:** BLOC 220

**Speaker:** Jose Burgos Gil, ICMAT, Madrid

**Title:** *Arithmetic of Toric Varieties, Lecture 1.*

**Abstract:** Abstract: Toric varieties form a very rich family of algebraic varieties that provide examples where explicit computations can be made. There is a toric dictionary that translates algebro-geometric concepts to combinatorial concepts. With this dictionary many algebro-geometric quantities can be computed. For example the degree of an ample line bundle on a toric variety is essentially given by the volume of an associated convex polytope. In joint work with P. Philippon and M. Sombra we have extended the toric dictionary to relate arithmetic properties with convex analytical properties. For example the height of a toric variety with respect to a positive metrized line bundle can be computed as the integral of a convex function on the associated polytope.

The minicourse will consist of three lectures:

Lecture 1: Overview of the theory of toric varieties.

Lecture 2: The theory of heights and the analogy between geometry and arithmetic.

Lecture 3: Arithmetic properties of toric varieties.

Most of the material of the course is in the book:

Burgos Gil, José Ignacio; Philippon, Patrice; Sombra, Martín Arithmetic geometry of toric varieties. Metrics, measures and heights. Astérisque No. 360 (2014).

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

**Location:** BLOC 220

**Speaker:** Nicolas Matte Bon, ETH Zurich

**Title:** *Orderable groups arising from Cantor dynamical systems*

**Abstract:** To every homeomorphism of the Cantor set, we associate a group of homeomorphisms of the real line. It is defined by an action on the mapping torus of the dynamical system which preserve each orbit of the suspension flow. I will explain how this produces a class of finitely generated simple groups of homeomorphisms of the real line, and investigate further properties of this construction.

**Time:** 6:00PM - 7:00PM

**Location:** BLOC 220

**Speaker:** Dr. Ivan Ivanov, Department of Vet Med - Physiology & Pharmacology, TAMU

**Title:** *Mathematical Models of Gene Regulatory Networks*

**Abstract:** The Central Dogma of the Molecular Biology describes the flow of information in the living cell. While the complex biochemical reactions underlying the cell functions can be modeled by stochastic differential equations those models have very little practical value, especially in situations where one would like to control for undesired cell phenotypes, e.g. cancer. We will discuss how the complex biochemical reactions can be projected onto the gene plane. The resulting gene regulatory network provides a fruitful ground for mathematical formalizations of the cell regulatory dynamics. One of the potential mathematical models, the Boolean Network model, will be discussed in detail.

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