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Seminars and Colloquiums
for the week of August 29, 2016


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

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

Monday, August 29th

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 $B(l_2(X))$.

TITLE: Dynamics of Biological Invasions
SPEAKER: Mahir Demir
TIME: 2:30pm – 3:20pm
ROOM: Ayres G003

Tuesday, August 30th

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.

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

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

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.

last updated: September 2016

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