# Events for 11/01/2019 from all calendars

## Probability Seminar

**Time:** 11:30AM - 12:30PM

**Location:** BLOC 628

**Speaker:** Quan Zhou, TAMU (Statistics)

**Title:** *Optimal detection of a drifting Brownian coordinate*

**Abstract:** Given a stochastic process X_t, how to find a stopping time \tau that maximizes the expectation of some reward function, say G(X_\tau), is known as an optimal stopping problem. Two famous examples are the secretary problem and the pricing of American options. Interestingly, continuous-time optimal stopping problems can often be converted to free-boundary PDE problems. The primary goal of this talk is to introduce the theory of optimal stopping using a class of problems which we refer to as “optimal detection of a drifting Brownian coordinate”: Imagine N independent Brownian motions. One of them has a nonzero drift while all the others are just standard Brownian motions. The question is how to find out which one is drifting as soon as possible. This problem can be formulated in many ways. In this talk we will focus on one particular formulation as an optimal stopping problem and solve the corresponding free boundary problem. Some other formulations will be briefly discussed as well. We will also mention applications of the optimal stopping theory (and more generally stochastic optimization) in statistics.

## Postdoc Lunch Time Talks

**Time:** 12:00PM - 12:20PM

**Location:** BLOC 220

**Speaker:** Samuel Harris, Texas A&M University

**Description:**

Title: Synchronous quantum correlations

Abstract:Synchronous correlations are a special subset of the usual quantum bipartite correlations. These synchronous correlations are of special relevance due to their connection with the weak Tsirelson problem in quantum information theory (equivalently, Connes' embedding problem in operator algebras). In this talk I will discuss some of the very recent advances in what we know about the synchronous correlation sets (specifically, in the finite-dimensional and the commuting operator models) and directions for future work.

## Postdoc Lunch Time Talks

**Time:** 12:35PM - 12:55PM

**Location:** BLOC 220

**Speaker:** Arman Darbinyan, Texas A&M University

**Description:**

Title: Group theory and computability

Abstract:The first part of my talk will be a review of some of the main results and connections between group theory and computability. After, I will discuss my recent results in this direction.

## Algebra and Combinatorics Seminar

**Time:** 3:00PM - 3:50PM

**Location:** BLOC 628

**Speaker:** Byeongsu Yu, Texas A&M University

**Title:** *Generalized Ishida Complex*

**Abstract:** Today, we will discuss the generalized Ishida complex. Masa-nori Ishida devised the Ishida complex to calculate local cohomology over the maximal ideal of a normal affine semigroup ring. We generalized this to calculate the local cohomology over all monomial supporting ideal. First of all, we will recall the definition of local cohomology and Čech Complex method. Then, we will investigate the properties of an affine monoid. Actually, an affine monoid can be viewed as a ring or as a polyhedral complex. A combination of these viewpoints allows us to have a cochain complex. This cochain complex comes from the polyhedral cone structure of the monomial ideal. Lastly, we will sketch to prove a statement that Generalized Ishida's complex calculates the local cohomology on affine semigroup ring over any monomial supporting ideal.

## Student Working Seminar in Groups and Dynamics

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

**Location:** BLOC 605AX

**Speaker:** James O'Quinn

**Title:** *An Ergodic approach to Sárközi's theorem*

**Abstract:** In order to demonstrate the usefulness of ergodic theory techniques to solve problems in number theory, I will present a proof for a general version of Sárközi's theorem using basic techniques in ergodic theory. This also gives an example of Furstenberg's Correspondence principle discussed in the previous talk.

## Geometry Seminar

**Time:** 4:00PM - 4:50PM

**Location:** BLOC 628

**Speaker:** Margaret Regan, Notre Dame

**Title:** *Applications of Parameterized Polynomial Systems.*

**Abstract:** Many problems in computer vision and engineering can be formulated using a parameterized system of polynomials which must be solved for given instances of the parameters. Due to the nature of these applications, solutions and behaviour over the real numbers are those that provide meaningful information for the system. This talk will describe using homotopy continuation within numerical algebraic geometry to solve these parameterized polynomial systems. It will also discuss applications regarding 2D image reconstruction in computer vision and 3RPR mechanisms in kinematics.