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# Events for September 12, 2018 from General and Seminar calendars

## Noncommutative Geometry Seminar

**Abstract:** I will discuss a class of Dirac-type operators, called equivariant Callias-type operators, on manifolds equipped with a Lie group action, where the orbit space is non-compact. It turns out that these operators are Fredholm with an index in the K-theory of the group C*-algebra and can be constructed by adding an ordinary (non-Fredholm) Dirac operator to an element of the K-theory of the equivariant Higson corona of the manifold. One can apply the index theory of such operators to prove an obstruction theorem for invariant metrics of positive scalar curvature.

## First Year Graduate Student Seminar

## AMUSE

**Abstract:** The topic of differential equations is an ever growing one. However, as in many mathematical problems, numerical methods are extremely useful, if not necessary. In this talk, we will explore the use numerical methods to solve differential equations, how two polynomials can be considered orthogonal, and how we can use a set of orthogonal polynomials to approximate the solution to differential equations, as well as the efficacy and limits of doing so. In short, one is able to solve an arbitrary linear differential operator with appropriate initial and/or boundary values to 6-16 decimal places depending on the difficulty of the problem and how many polynomials are used in the solution.

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

**Location:** BLOC 628

**Speaker:** Hao Guo, Texas A&M University

**Title:** *Index of Equivariant Callias-Type Operators*

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

**Location:** BLOC 628

**Speaker:** Ola Sobieska-Snyder, Ayo Adeniran, and Peter Howard

**Title:** *Outreach opportunities and other things students should start doing now to prepare for the job search*

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

**Location:** BLOC 220

**Speaker:** Jay Standridge, Undergraduate Student, Department of Aerospace Engineering, TAMU

**Title:** *Approximating the solutions to differential equations using orthogonal polynomials*