# Events for 09/25/2019 from all calendars

## Quantum Symmetries Seminar

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

**Location:** BLOC 111

**Speaker:** Qing Zhang, Texas A&M University

**Title:** *Exercise 2*

## Inverse Problems and Machine Learning

**Time:** 12:00PM - 1:00PM

**Location:** BLOC628

**Speaker:** Weston Baines, Texas A&M

**Title:** *Deep neural network for source detection in 2D high noise emission problems*

**Abstract:** Source detection in high noise environments is crucial for single-photon emission computed tomography (SPECT) medical imaging and especially for homeland security applications. In the latter case, one deals with detection of low emission nuclear sources in the presence of significant background noise (with SNR < 0.01). Direction sensitivity is needed to achieve this goal. Collimation, used for that purpose in standard gamma-cameras is not an option. Instead, Compton cameras are used. Backprojection methods enable detection in a random uniform background. In most practical applications, however, the presence of cargo violates this assumption and renders backprojection methods ineffective. A deep neural network is implemented for the task that exhibits higher sensitivity and specificity than the backprojection techniques in a low scattering case and works well when presence of cargo makes those techniques fail. This is joint work with P. Kuchment (Math) and J. Ragusa (Nuclear Eng.)

## Mathematical Physics and Harmonic Analysis Seminar

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

**Location:** BLOC 628

**Speaker:** Lior Alon, Technion - Israel Institute of Technology

**Title:** *On a CLT conjecture for the nodal statistics of quantum graphs*

**Abstract:** Understanding statistical properties of Laplacian eigenfunctions in general and their nodal sets in particular have an important role in the field of spectral geometry, and interest both mathematicians and physicists. A quantum graph is a system of a metric graph with self adjoint Schrodinger operator acting on it. In the case of quantum graphs it was proven that the number of points on which each eigenfunction vanish also known as the nodal count is bounded away from the spectral position of the eigenvalue by a topological quantity, the first Betti number of the graph. A remarkable result by Berkolaiko and Weyand (with another proof for discrete graphs by Colin de Verdiere) showed that the nodal surplus is equal to a magnetic stability index of the corresponding eigenvalue. Both from the nodal count point of view and from the physical magnetic point of view, it is interesting to consider the distribution of these indices over the spectrum. In our work we show that such a density exist and define a nodal surplus distribution. Moreover this distribution is symmetric, which allows to deduce the Betti number of a graph from its nodal count. A further result proves that the distribution is binomial with parameter half for a certain large family of graphs. The binomial distribution satisfy a CLT convergence, and a numerical study indicates that the CLT convergence is independent of the specific choice of the growing family of graphs. In my talk I will talk about our latest results extending the number of families of graphs for which we can prove the CLT convergence. Joint work with Ram Band and Gregory Berkolaiko.

## Groups and Dynamics Seminar

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

**Location:** BLOC 220

**Speaker:** Frank Lin, UT Austin

**Title:** *A topological dynamical system with two different positive sofic entropies*

**Abstract:** Dynamical entropy is an important tool in classifying measure-preserving or topological dynamical systems up to measure or topological conjugacy. Classical dynamical entropy theory, of an action of a single transformation, has been studied since the 50s and 60s. Recently Lewis Bowen and Kerr-Li have developed entropy theory for actions of sofic groups. Although a conjugacy invariant, sofic entropy in general appears to be less well-behaved than classical entropy. In particular, sofic entropy may depend on the choice of sofic approximation, although only degenerate examples have been known until now. We present an example, inspired by hypergraph 2-colorings from statistical physics literature, of a topological dynamical system with two different positive topological sofic entropies corresponding to different sofic approximations. The measure-theoretic case remains open.

## Maxson Lecture Series

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

**Location:** BLOC 117

**Speaker:** David A. Cox, Amherst College

**Title:** *Maxson Lecture #1: Moment Maps of Toric Varieties, Linear Precision, and Maximum Likelihood Degree One*

**Abstract:** I will begin with a question about the moment maps of toric varieties (from symplectic geometry). To get some preliminary insight, I will relate this question to the concept of strict linear precision (from geometric modeling). However, the best result so far uses a result of June Huh on maximum likelihood degree one (from algebraic statistics). I will also discuss the more general notion of rational linear precision and pose some open problems. This is joint work with Patrick Clarke of Drexel University.

## First Year Graduate Student Seminar

**Time:** 5:30PM - 6:30PM

**Location:** Blocker 628

**Title:** *Adjusting to Graduate School*