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# Events for January 31, 2018 from General and Seminar calendars

## Number Theory Seminar

**Abstract:** Let f(x) = x^k+a in Z[x] for k \geq 2. Consider the family of dynamical systems given by the action of f on F_p as p varies among primes. The question of how and in what sense this family approximates a random family of dynamical systems has been studied extensively, motivated in part by Pollard's "rho" algorithm for integer factorization. We show that for most choices of a, the cycle structure in this family is "as random as possible" in an appropriate sense. As a corollary, we show that most members of these families have many cycles. This is joint work with Derek Garton.

## Numerical Analysis Seminar

**Abstract:** “We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipshitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Eduard Feireisl and Simon Markfelder.

## Groups and Dynamics Seminar

**Abstract:** I will explain how seemingly unrelated objects: the group G of intermediate growth constructed by the speaker in 1980, the aperioidc order, and the theory of (random) Schroediinger operator can meet together. The main result, to be discussed, is based on a joint work with D.Lenz and T.Nagnibeda. It show that a random Markov operator on a family of Schreier graphs of G associated with the action on a boundary of a binary rooted tree has a Cantor spectrum of the Lebesgue measure zero. This will be used to gain some information about the spectrum of the Cayley graph. The main tool of investigation is given by a substitution, that, on the one hand, gives a presentation of G in terms of generators and relations, and, on the other hand, defines a minimal substitutional dynamical system which leads to the use of the theory of random Shroedinger operator. No special knowledge is assumed, and the talk is supposed to be easily accessible for the audience.

## Faculty Meeting

## AMUSE

**Abstract:** Each year, millions of people worldwide are infected with the influenza virus resulting in a significant public health and economic burden. Although the transmission and prevention of influenza involves many complicating factors, simple mathematical models can provide insight into the dynamics of epidemics and help public health officials make decisions about public health policy. In this talk, I will present a simple model for influenza transmission including vaccination and discuss some basic techniques for epidemiological modeling.

**Time:** 1:15PM - 2:15PM

**Location:** BLOC 220

**Speaker:** Andrew Bridy, Texas A&M University

**Title:** *The cycle structure of unicritical polynomials in finite fields*

**URL:** *Link*

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

**Location:** BLOC 628

**Speaker:** Christian Klingenberg, Würzburg University

**Title:** *The inititial value problem for the multidimensional system of compressible gas dynamics may have infinitely many weak solutions*

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

**Location:** BLOC 220

**Speaker:** Rostislav Grigorchuk, Texas A&M

**Title:** *Group of intermediate growth, aperiodic order, and Schroedinger operators.*

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

**Location:** BLOC 117

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

**Location:** BLOC 220

**Speaker:** Dr. Glenn Lahodny, Texas A&M University, Department of Mathematics

**Title:** *It's Flu Season! (A Mathematical Model of Influenza)*