**Seminars and Colloquiums**

for the week of March 28, 2016

for the week of March 28, 2016

*SPEAKER:*

Ben Levy, UTK, Monday

Eleanor Abernethy, UTK, Monday

Yaozhong Hu, University of Kansas, Tuesday

Johnny Guzman, Brown, Wednesday

Wenqiang Feng, UTK, Thursday

Kevin Sonnanburg, UTK, Thursday

Roger Barnard, Texas Tech, Friday

**Monday, March 28th **

DOCTORAL DEFENSE

TITLE: Modeling Feral Hogs in Great Smoky Mountains National Park

SPEAKER: Ben Levy

TIME: 1:30pm – 2:30pm

ROOM: Ayres 405

His committee consists of Professors: Lenhart (Chair), Collins, Armsworth (EEB),

and Odoi (Biomedical and Diagnostic Sciences)

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Critical Spectra

SPEAKER: Eleanor Abernethy, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

Spectra are a classical way to understand the geometry of compact Riemannian manifolds in Differential Geometry. Two well-known spectra are the Laplace spectrum and the length spectrum. A relatively new spectrum is the covering spectrum, developed by Sormani and Wei (2003), which utilizes delta-covers of a compact geodesic space and singles out values of ?? where the covering spaces ??_?? ? ??_??? for all ???>??. More recently, Plaut and Wilkins (2012) developed the homotopy critical spectrum which arises from a discrete analog of the fundamental group construction for a compact metric space. It is already known that the covering and homotopy critical spectra are essentially the same on compact geodesic spaces. However, the homotopy critical spectrum is defined in the more general setting of metric spaces. de Smit, Garnet and Sutton (2010) extended the notion of the covering spectrum to any metric space. I will present results of comparing the definitions of the homotopy critical spectrum and the de Smit/Garnet/Sutton formulation of the covering spectrum on general metric spaces. I will also outline a strategy for extending this classification to Uniform Topological Spaces in which this will be the Entourage Critical Spectrum.

**Tuesday, March 29th **

STOCHASTICS SEMINAR

TITLE: Convergence in density of nonlinear Gaussian functionals

SPEAKER: Yaozhong Hu, University of Kansas

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

In this talk I will present some results on the convergence in densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. The idea is to use Malliavin calculus. Application to polynomials of Gaussian time series will also be presented.

** Wednesday, March 30th **

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Finite element methods for high contrast interface problems

SPEAKER: Johnny Guzman, Brown

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

We present two different finite element methods for second order elliptic problems with interfaces. The difficulty in approximation solutions of these problems is that solutions are not smooth across the interface. One approach is to refine the mesh near the interface. Another approach is to work on a fixed mesh that is not aligned with the interface and modify the standard method. We take the second approach as this is more appropriate for time dependent problems where the interface moves.

**Thursday, March 31st **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Well-Posedness and Numerical Analysis for Thin Film Epitaxy Equation with Slope Selection

SPEAKER: Wenqiang Feng, UTK

TIME: 2:00pm - 3:00pm

ROOM: Ayres 113

In the first part of this talk I will review the Well-Posedness in [LI-LIU-EJAM] where the Galerkin spectral approximations are studied to provide a priori bounds for proving the well-posedness. In the second part, I will present the convergence analysis for the preconditioned steepest descent method. By using the energy dissipation property, we derive the $L^p$ bound for the solution and upbound for the second derivative of the energy to investigate the convergence properties. Many numerical simulations for thin film epitaxy with slope selection are carried out to confirm part of the analysis. Moreover, we present, for the first time, the numerical simulations for $H^{-1}$ gradient flows of thin film epitaxy by using the proposed method.

GRADUATE STUDENT SEMINAR

TITLE: Math Circles

SPEAKER: Kevin Sonnanburg, UTK

TIME: 3:40pm – 4:30pm

ROOM: Ayres G004

Math Circles is an outreach program to connect mathematicians with K-12 students to share in the exploration deeper concepts and more creative problem solving. There are almost 200 nationwide, but none in Tennessee. The program offers resources and funding to train teams and help tailor a Math Circle to local needs. I will describe the available resources and some possible program structures to see who might be interested in starting a local Circle.

**Friday, April 1st**

COLLOQUIUM

TITLE: Bohr's phenomenon for power series

SPEAKER: Roger Barnard, Texas Tech

TIME: 3:30pm-4:30pm

ROOM: Ayres 405

*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:**

3/14/2016 - spring break