**Seminars and Colloquiums**

for the week of August 29, 2016

for the week of August 29, 2016

*SPEAKER:*

Jerzy Dydak, UTK, Monday

Mahir Demir, UTK, Monday

Camila Reyes (SACNAS Chapter Meeting), UTK, Tuesday

Yu-Ting Chen, UTK, Tuesday

Faruk Yilmaz, UTK, Wednesday

Marie Jameson, UTK, Friday

*TEA TIME
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted By: Ibrahim Aslan*

**Monday, August 29th **

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Hybrid scale spaces and duality

SPEAKER: Jerzy Dydak

TIME: 2:30pm – 3:20pm

ROOM: Ayres 114

Most of the talk is based on joint work with my former PhD students: Kyle Austin and Michael Holloway. Its purpose is to investigate the duality between large scale and small scale. It is done by creating a connection between C*-algebras and scale structures.

In the commutative case we consider C*-subalgebras of $C^b(X)$, the C*-algebra of bounded complex-valued functions on $X$. Namely, each C*-subalgebra $\mathscr{C}$ of $C^b(X)$ induces both a small scale structure on $X$ and a large scale structure on $X$. The small scale structure induced on $X$ corresponds (or is analogous) to the restriction of $C^b(h(X))$ to $X$, where $h(X)$ is the Higson compactification.

The large scale structure induced on $X$ is a generalization of the $C_0$-coarse structure of N.Wright. Conversely, each small scale structure on $X$ induces a C*-subalgebra of $C^b(X)$ and each large scale structure on $X$ induces a C*-subalgebra of $C^b(X)$. To accomplish the full correspondence between scale structures on $X$ and C*-subalgebras of $C^b(X)$ we need to enhance the scale structures to what we call hybrid structures. In the noncommutative case we consider C*-subalgebras of bounded operators $B(l_2(X))$.

MATH BIOLOGY SEMINAR

TITLE: Dynamics of Biological Invasions

SPEAKER: Mahir Demir

TIME: 2:30pm – 3:20pm

ROOM: Ayres G003

** Tuesday, August 30th **

SACNAS UTK CHAPTER

TITLE: Chapter Interest Meeting

SPEAKER: Camila Reyes

TIME: 11:30am – 12:30pm

ROOM: Claxton 105 at NIMBIOS

SACNAS stands for “The Society for Advancement of Chicanos/Hispanics and Native Americans in Science.” It’s an inclusive organization promoting diversity in STEM fields. It started as an organization to foster the success of Chicano/Hispanic and Native American scientists, from college students to professionals, in attaining advanced degrees, careers, and positions of leadership in STEM.

The chapter is open to everyone (students and faculty) who is interested in joining. If you join before September 28th you can apply for a waived membership to the national organization.

Pizza will be served. Please bring your own beverage.

STOCHASTICS SEMINAR

TITLE: KPZ equation

SPEAKER: Yu-Ting Chen

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

The Kardar-Parisi-Zhang stochastic PDE is expected to describe universally the fluctuations of weakly asymmetric interface growth. Its ill-posedness challenges the classical Ito theory for stochastic integration, and continues to inspire the development of new techniques for stochastic analysis.

This talk is an introductory discussion of the KPZ stochastic PDE. I will start with the physical background of the Kardar-Parisi-Zhang equation and discuss some recent progress in stochastic analysis in this field.

**Wednesday, August 31st **

ANALYSIS SEMINAR

TITLE: "Approximation of Invariant Subspaces in some Dirichlet-type spaces", part II

SPEAKER: Faruk Yilmaz, UTK

TIME: 2:30pm – 3:20pm

ROOM: G003 In this talk, I will define D_alpha} spaces and give some known properties of these spaces. In particular I will focus on D_2. When the convergence of a sequence of subspaces is mentioned, this is actually a statement about the convergence of the corresponding sequence of projections. In 1972, Korenblum gave the complete characterization of the invariant subspaces of the multiplication operator on D_2. I will prove a theorem about approximation of invariant subspaces of D_2 in terms of finite co-dimensional ones.

**Friday, September 2nd **

COLLOQUIUM

TITLE: Modular forms and related objects

SPEAKER: Marie Jameson, UTK

TIME: 3:30pm-4:30pm

ROOM: Ayres 405

In this talk, we will examine modular forms, which are holomorphic functions on the upper half of the complex plane that satisfy certain transformation properties. To start, we will review some interesting combinatorial questions which serve as motivation for this study; then we will discuss how to use the theory of $q$-series and modular forms to understand these mathematical questions, as well as others. Finally, we will explore the structure inherent in the theory of modular forms and related objects.