**Seminars and Colloquiums**

for the week of September 1, 2014

for the week of September 1, 2014

*SPEAKER:*

Prof. Xia Chen, Tuesday

Prof. Max Jensen, Sussex, Wednesday

Prof. Mike Frazier, Thursday

Prof. Fernando Schwartz, Thursday

Prof. Stefan Richter, Friday

Prof. Max Jensen, Sussex, Friday

**Tuesday, September 2**

PROBABILITY SEMINAR

TIME: 2:10 - 3:25 p.m.

ROOM: Ayres 112

SPEAKER: Prof. Xia Chen, UTK

TITLE: Asymptotics for the principle eigenvalue of N-body problem: a large deviation approach

ABSTRACT: The *N-*body problem is described by a *N*d-dimensional Schrodinger operator with the potential that symbols a pairwise interaction among *N* particles in the space. One of the central topics in *N*-body problem is the spectral structure of the Schrodinger operator for its relevance to the energy quantification of the system. In this talk, we shall represent an asymptotic behavior of the principle eigenvalue of the Schrodinger operator as the number of the particles increases and the mass of each particle shrinks. Our proof is probabilistic and is relevant to Donsker-Varadhan large deviation principle.

The talk is based an on-going project collaborated with Tuoc Van Phan and Tadele Mengesha.

**Wednesday, September 3**

COMPUTATIONAL/APPLIED MATH SEMINAR

TIME: 3:35 - 4:25 p.m.

ROOM: Ayres 113

SPEAKER: Prof. Max Jensen, Sussex

TITLE: Wellposedness and Finite Element Convergence for the Joule Heating Problem

ABSTRACT: The stationary Joule heating problem is a two way coupled system of non-linear partial differential equations modelling the heat and electrical potential in a body. The electrical current acts as a heat source in a resistive material while the temperature feeds back to the electrical potential through the electrical conductivity. Joule heating is important in many micro-electromechanical systems, where the effect is used to achieve very exact positioning at the micro scale. In applications boundary conditions of mixed type are typically used.

In this talk we present the existence proof for finite energy solutions of the Joule heating problem in three dimensions with mixed boundary conditions, using only very mild assumptions on the computational domain and the data. In particular, we show how previously established results can be extended to mixed boundary conditions. Furthermore, we prove strong convergence (of subsequences in case of non-unique exact solutions) of conforming finite element approximations.

Under the additional assumption of a so-called creased domain together with a sufficiently weak temperature dependency in the electrical conductivity we also prove optimal global regularity estimates together with local estimates guaranteeing smooth solutions away from the boundary given smooth data. We further discuss a priori and a posteriori error bounds for conforming finite element approximations on shape regular meshes.

The presented material is joint work with Axel Målqvist (Uppsala, Sweden).

**Thursday, September 4**

DIFFERENTIAL EQUATIONS SEMINAR

TIME: 2:10 - 3:00 p.m.

ROOM: Ayres 113

SPEAKER: Prof. Mike Frazier, UTK

TITLE: Introduction to Besov Spaces, Part II

ABSTRACT: We continue our introduction to Besov spaces. We give the general definition of Besov spaces for all index parameters, and discuss some of the imbeddings between Besov spaces and Sobolev spaces.

JUNIOR COLLOQUIUM

TIME: 3:35 - 4:25 p.m.

ROOM: Ayres 405

SPEAKER: Prof. Fernando Schwartz, UTK

TITLE: Topology Backs Alternative Medicine Claim

ABSTRACT: The holistic concept in alternative medical practice upholds that “all of people’s needs should be taken into account.” In other words, the body is seen as a whole. The holistic point of view can be scientifically validated by determining whether different bodily variables are related to one another. In this talk we provide strong evidence supporting this claim. We show the existence of at least one fully non-linear relationship involving two bodily variables.

Pizza will be available at 3:10 p.m.

**Friday, September 5**

ANALYSIS SEMINAR

TIME: 2:30 - 3:20 p.m.

ROOM: Ayres 111

SPEAKER: Prof. Stefan Richter, UTK

TITLE: Hankel operators and invariant subspaces of the Dirichlet shift, Part II

COLLOQUIUM

TIME: 3:35 - 4:25 p.m.

ROOM: Ayres 405

SPEAKER: Prof. Max Jensen, Sussex

HOST: Xiaobing Feng

TITLE: Hamilton-Jacobi-Bellman equations and their numerical approximations

ABSTRACT: Hamilton-Jacobi-Bellman (HJB) equations is a class of second order fully nonlinear PDEs which describe how the cost of an optimal control problem changes as problem parameters vary. Applications can be found in engineering, finance and science as well as in geometric PDE theory. This talk will first introduce HJB equations in the context of stochastic optimal control using dynamic programming (Bellman Principle) and then briefly discuss PDE theory for HJB equations. The focus of the remaining talk will be on explaining how Galerkin methods can be adapted to solve these equations efficiently. In particular, it will be discussed how the convergence argument by Barles and Souganidis for finite difference schemes can be extended to Galerkin finite element methods to ensure convergence to viscosity solutions. A key question in this regard is the formulation of the consistency condition. Due to the Galerkin approach, coercivity properties of the HJB operator may also be satisfied by the numerical scheme. In this case one achieves besides uniform also strong H1 convergence of numerical solutions on unstructured meshes.

*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:**