# Events for October 25, 2017 from General and Seminar calendars

## Postdoc Lunch Time Talks

Time: 12:00PM - 12:20PM

Location: BLOC 220

Speaker: Yuan Zhang, Texas A&M University

Description: Title: Stationary Harmonic Measure and DLA in the Upper half Plane

Abstract: In this talk, we introduce the stationary harmonic measure in the upper half plane. By controlling the bounds of this measure, we are able to define a continuous diffusion limit aggregation (DLA) in the upper half plane with absorbing boundary conditions. We prove that the growth rate of the longest arm in the DLA with respect to time $t$ is no more than $o(t^{2+\epsilon})$.

## Postdoc Lunch Time Talks

Time: 12:35PM - 12:55PM

Location: BLOC 220

Speaker: Julia Plavnik, Texas A&M University

Description: Title: Mathematics of Topological Quantum Computation

In this talk, we will give an overview to some of the basic mathematical ingredients needed to study topological quantum computing and topological phases of matter. We will provide a gentle introduction to the notions of braids and modular categories, focusing on their properties and connections instead of formal definitions. We will also discuss how some questions arising from physics or quantum information can be translated to mathematical problems using these concepts.

## Postdoc Lunch Time Talks

Time: 12:55PM - 1:15PM

Location: BLOC 220

Speaker: Rick Lynch, Texas A&M University

Description: Title: Preserving a certain operator property under subgaussian maps

Abstract: In this talk, I will discuss the following result. As long as an operator $\mathbf{D}$ stays bounded away from zero in norm on $S$ and a provided map ${\boldsymbol \Phi}$ comprised of i.i.d. subgaussian rows has number of measurements at least proportional to the square of $w(\mathbf{D}S)$, the Gaussian width of the related set $\mathbf{D}S$, then with high probability the composition ${\boldsymbol \Phi} \mathbf{D}$ also stays bounded away from zero in norm on $S$ with bound proportional to $w(\mathbf{D}S)$. The null space property is preserved w.h.p. under such subgaussian maps as a consequence, and there might be other potential applications in dimension reduction analysis. This is joint work with Peter G. Casazza (University of Missouri) and Xuemei Chen (University of San Francisco).

## Student Working Seminar in Groups and Dynamics

Time: 1:00PM - 2:00PM

Location: BLOC 628

Speaker: Roman Kogan

Title: Finite-state automata and measures

Abstract: The idea of self-similarity has been prominently used in group theory ever since the introduction of the Grigorchuk group, generated by states of a finite-state machine with output, to answer Milnor's question on intermediate growth of groups. Similar ideas can be applied to the study of measures on the space of sequences in a finite alphabet to define finite-state measures. These measures generalize Bernoulli, Markov and k-step Markov measures in a natural way, and are preserved by the action of invertible finite-state automorphisms. We introduce and briefly discuss the properties of these measures, such as when they are k-step Markov, and when their image under non-invertible automorphisms is finite-state.

## Postdoc Lunch Time Talks

Time: 1:15PM - 1:35PM

Location: BLOC 220

Speaker: Laura Saavedra, Texas A&M University

Description: Title: A stabilized Lagrange-Galerkin method for the simulation of turbulent flows.

Abstract: We present stabilized Lagrange-Galerkin method to integrate the incompressible Navier Stokes equations at high Reynolds numbers. The stabilization of the conventional Lagrange-Galekin method is done via a local projection technique for inf-sup stable finite elements. We prove that the stabilized method has the same accuracy as the standard one. The numerical results shows that our method is stable and can predict the behavior of high Reynolds flows.

## Noncommutative Geometry Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Suleyman Kagan Samurkas, Texas A&M University

Title: Bounds for the rank of the finite part of operator $K$-Theory

Abstract: We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy classes of finite order elements in the group. The upper bound is based on the amount of torsion elements in the group. We use the lower bound to give lower bounds for the structure group $S(M)$ and the group of positive scalar curvature metrics $P(M)$ for an oriented manifold $M$. We define a class of groups called polynomially full groups'' for which the upper bound and the lower bound we derive are the same. We show that the class of polynomially full groups contains all virtually nilpotent groups. As example, we give explicit formulas for the ranks of the finite parts of operator $K$-theory groups for the finitely generated abelian groups, the symmetric groups and the dihedral groups.

## Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Giorgio Bornia, Texas Tech

Title: Some questions arising in PDE-constrained optimal control and numerical linear algebra

Abstract: The talk will be divided in two parts. In the first one, we address some issues arising in a certain class of boundary optimization problems. Common boundary optimal control problems yield a mismatch between the regularity of solutions on the domain and their boundary data. We discuss a reformulation of these problems with a lifting approach whose goal is to fix this regularity mismatch. Moreover, this approach provides additional benefits when applied to constraints characterized by compatibility conditions on the boundary data, such as those arising for the incompressible Navier-Stokes equations. In the second part of the talk, we discuss an analysis of preconditioning schemes for the numerical solution of Rayleigh-Bénard convection problems discretized with inf-sup stable finite element spaces. The analysis is carried out using a notion of field-of-values (FOV) equivalence between the preconditioner and the system matrix. Numerical results are discussed for both topics.

## Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Guoliang Yu, Texas A&M

Title: Dynamic dimension and K-theory

Abstract: I will introduce a notion of dynamic asymptotic dimension for group actions and discuss its application to K-theory. This is joint work with Erik Guentner and Rufus Willett. I will make the talk accessible to graduate students.

## Postdoc Colloquium Series

Time: 4:00PM - 5:00PM

Location: Bloc 220

Title: Radiation fields for wave equations

Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a variety of contexts, starting with the familiar one dimensional wave equation and moving to the semilinear wave equation in three dimensions, the linear wave equation on the exterior of a non-rotating black hole, and then on a class of time-dependent spacetimes. Although the object of study is the same in each case, the methods used are quite different in the time-independent and time-dependent settings.

## First Year Graduate Student Seminar

Time: 5:30PM - 6:30PM

Location: BLOC 628

Speaker: Student Panel

Title: Panel discussion: preparing for qualifying exams

## AMUSE

Time: 6:00PM - 00:00AM

Location: BLOC 220

Speaker: Dr. Darren Hartl, Texas A&M University, Department of Aerospace Engineering

Title: Advantageous couplings: the science and math behind multifunctional materials and structures

Abstract: The development of active and adaptive aerospace structures based on the behavior of unique materials has been considered with great fervor especially since the various federally funded efforts of the 1990's. What is new and highly enabling is the increased fidelity of three-dimensional mathematical models and especially the implementation of these models into ever more comprehensive design frameworks. Given the sustained improvement of such design tools, full analysis-driven optimization considering such concepts as coupled fields and uncertainty may soon become common practice in the multifunctional structure design community. This will enable both the increased performance of current concepts and an expansion in creativity regarding the kinds of material and structural configurations considered. This talk will review recent multifunctional material and structures modeling and design efforts with which Dr. Hartl has been involved over the last three years as well as his current research efforts at Texas A&M. Some of the advances in multifunctional aerospace structural modeling and design will be highlighted. Design concepts such as liquid metal-based reconfigurable antennas and morphing components will be described, and design approaches leveraging evolutionary genetic programming will be shared.”