Un of Tenn | Math Department

Seminars and Colloquiums
for the week of January 21, 2013

Speakers:

Dr. Bangti Jin, Texas A&M, Tuesday
Dr. Shi Chen, Post Doc, Vet School, Wednesday
Prof. Stefan Richter, Wednesday
Mr. Kyle Austin, Thursday
Dr. Pablo Seleson, University of Texas, Austin, Thursday

*** Tea Time this week will be Tuesday - Friday at 3:00 pm.
Hosted this week by Jochen Denzler and David Anderson. Everyone is welcome! ***

Tuesday, January 22

COLLOQUIUM
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Bangti Jin, Texas A&M
TITLE: An Invitation to Fractional Differential Equations
ABSTRACT: In this talk, we consider differential equations with a fractional-order derivative, which arise in many practical applications, e.g., underground flow and material science, and have attracted much interest in the past few decades. We will describe the basics of fractional calculus, especially the Riemann-Liouville fractional derivative and Caputo fractional derivative and their properties, and discuss the influence of the nonlocal nature of the fractional derivatives on the solution behavior, inverse problems and numerical analysis. These different aspects will be illustrated with two "simple" examples, i.e., the time-fractional diffusion problem and the fractional Sturm-Liouville problem.

Refreshments will be served at 3:15 p.m.

Wednesday, January 23

MATH BIOLOGY SEMINAR
TIME: 12:20 - 1:10 p.m.
ROOM: Ayres 114
SPEAKER: Shi Chen, Post Doc, Vet School
TITLE: Ecological Models and Data in R, continued

ANALYSIS SEMINAR
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 112
SPEAKER: Prof. Stefan Richter
TITLE: Weak products of spaces of analytic functions

Thursday, January 24

TOPOLOGY SEMINAR
TIME: 9:40 – 10:30 a.m.
ROOM: Ayres Hall B004
SPEAKER: Mr. Kyle Austin
TITLE: Partitions of Unity
ABSTRACT: The purpose of this presentation is to introduce partitions of unity and their applications to topology and analysis. This should give an interesting new point of view for normal and paracompact spaces. The presentation will follow the paper "Partitions of Unity" by Jerzy Dydak. In particular, we will use partitions of unity to prove variants of Teitze Extension Theorem which in turn will be used to prove some classical results about normal and paracompact spaces. The notion of equicontinuous partitions of arbitrary functions will be introduced. We will use this idea to create certain partitions of unity with nice properties and to give a useful characterization of when a normal space is paracompact.

COLLOQUIUM
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Pablo Seleson, University of Texas, Austin
TITLE: Multiscale Material Modeling with Peridynamics
ABSTRACT: Multiscale modeling has been recognized in recent years as an important research field to achieve feasible and accurate predictions of complex systems. Peridynamics, a nonlocal reformulation of continuum mechanics based on integral equations, is able to resolve microscale phenomena at the continuum level. As a nonlocal model, peridynamics possesses a length scale which can be controlled for multiscale modeling. For instance, classical elasticity has been presented as a limiting case of a peridynamic model. In this talk, I will introduce the peridynamics theory and show analytical and numerical connections of peridynamics to molecular dynamics and classical elasticity. I will also present multiscale methods to concurrently couple peridynamics and classical elasticity, demonstrating the capabilities of peridynamics towards multiscale material modeling.

Refreshments will be served at 3:15 p.m.

If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.

If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu

Past notices: