**Seminars and Colloquiums**

for the week of April 10, 2017

for the week of April 10, 2017

*SPEAKER:*

Boris Goldfarb (SUNY-Albany), Monday

John Nolan, American University, Tuesday

Yunxiang Ren, Vanderbilt University, Wednesday

Daozhi Han, Indiana University, Wednesday

Stefan Schnake, UTK, Thursday

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, and Wednesday: Ayres 401
*

*Hosted by: Mustafa Elmas & Mitchell Sutton*

**Monday, April 10th**

TOPOLOGY/GEOMETRY SEMINAR

Title: The topological rigidity conjecture through controlled $G$-theory

Speaker: Boris Goldfarb (SUNY Albany)

Time: 2:30pm - 3:20pm

Room: 113 Ayres

Abstract: I will describe the joint work with Gunnar Carlsson on the old conjecture of Armand Borel in topology. The conjecture states that if a closed aspherical manifold $M$ is homotopy equivalent to another manifold then the two manifolds have to be homeomorphic. The aspherical condition is equivalent to the universal cover of $M$ being contractible, which is common in geometry. I will explain how this geometric statement is translated to algebra in the modern approach to Borel. We study the $K$-theoretic assembly map associated to $\pi_1 (M)$ by factoring it through a controlled version of Grothendieck's $G$-theory of the group ring $\mathbb{Z} \pi_1 (M)$. The $G$-theory turns out to be easier to compute and is equivalent to $K$-theory in very general geometric situations, for example when $\pi_1 (M)$ has finite decomposition complexity. If there is time, I will compare this method to the Farrell-Jones conjectures. Several crucial features of the method belong to “coarse geometry” that is very popular in Knoxville.

**Tuesday, April 11th**

STOCHASTICS/ PROBABILITY SEMINAR

Title: Dense classes of multivariate extreme value distributions

Speaker: John Nolan, American University

Time: 2:10pm-3:25pm

Room: 113 Ayres

Abstract: We explore tail dependence modeling in multivariate extreme value distributions through the use of the scale function. This allows combinations of distributions in a flexible way. The correspondences between the scale function and the spectral measure or the stable tail dependence function are given. Combining scale functions by simple operations, semi-parametric classes of laws are described and analyzed, and resulting nested and structured models are discussed. Finally, the denseness of each of these classes is shown.

Comparisons to multivariate stable laws are discussed. We end with a discussion of current work for computing and fitting multivariate extreme value laws with semi-parametric models via max projections.

This is joint work with Anne-Laure Fougeres and Cecile Mercadier at the University of Lyon.

**Wednesday, April 12th**

ANALYSIS SEMINAR

Title: Classification of Thurston-relation planar algebra

Speaker: Yunxiang Ren, Vanderbilt University

Time: 2:30pm-3:20pm

Room: 113 Ayres

Abstract: Planar algebras were introduced by Jones as a topological axiomatization of the standard invariants of subfactors. With this perspective, it is natural to understand subfactors through their skein theory, i.e, generators and relations (both algebraic and topological). In this talk, we will discuss the subfactor planar algebra generated by a 3-box with Thurston relation as a continuation of the classification program by skein theory proposed by Bisch and Jones. We give a full classification of such subfactors and explore these subfactors from their skein theory.

COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR

Title: Modeling and numerical simulations of two-phase flow in karstic geometry.

Speaker: Daozhi Han, Indiana University

Time: 3:35pm – 4:35pm

Room: 113 Ayres

Abstract: Multiphase flow phenomena are ubiquitous. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits, and in porous media must be considered together. Geometric configurations that contain both conduit and porous media are termed karstic geometry. In this talk, we derive a diffuse interface model for two-phase flow in karstic geometry utilizing Onsager's extremum principle. The model together with the interface boundary conditions satisfies a physically important energy law. We show that the model admits a global finite-energy weak solution which agrees with the regular solution provided the regular solution exists. Then we present a decoupled unconditionally energy-stable numerical scheme for solving this diffuse interface model. Finally we will discuss the design of second order accurate unconditionally stable schemes for solving diffuse interface models.

**Thursday, April 13th**

DIFFERENTIAL EQUATIONS SEMINARS

Title: A Vanishing Moment Method for Second-order Linear Elliptic PDEs in Non-divergence Form.

Speaker: Stefan Schnake, UTK

Time: 2:00pm-3:00pm

Room: 113 Ayres

Abstract: This talk will focus on the vanishing moment method for second order, linear, elliptic PDEs in non-divergence form whose coefficients are only continuous. These PDEs present themselves in the nonlinear Hamilton-Jacobi-Bellman equations, which have applications in stochastic optimal control and mathematical finance, as well as the linearization of the Mange-Amprere equations. The vanishing moment method seeks to approximate the second order PDE by a family of fourth order PDEs created by the addition of a small biharmonic term. Uniform H1 and H2 estimates will be given implying the convergence of the method. In addition, error estimates in the L2 and H1 norms will be shown.

*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:**

3/13/17 - Spring Break

Winter Break