**Seminars and Colloquiums**

for the week of February 13, 2017

for the week of February 13, 2017

*SPEAKER:*

Natalie Hobson, University of Georgia, Monday

Dr. Yizao Wang, University of Cincinnati, Tuesday

Delong Li, UTK, Wednesday

Remus Nicoara, UTK, Wednesday

Professor Hong Wang, University of South Carolina, Wednesday

Professor Lili Ju, University of South Carolina, Friday

Hung Tran, University of Wisconsin–Madison, Friday

*TEA TIME -
3:00 pm – 3:30 pm
Monday; Room: Ayres 4th Floor Common Area
Tuesday & Wednesday; Room: Ayres 401*

*Hosted by: Ibrahim Aslan & Xiaoyang Pan*

**Monday, February 13th **

ALEGEBRA SEMINAR

TITLE: Quantum Kostka and the rank on problem for sl_2m

SPEAKER: Natalie Hobson, University of Georgia

TIME: 2:30pm – 3:20pm

ROOM: Ayres 111

In this talk we will define and explore an infinite family of vector bundles, known as vector bundles of conformal blocks, on the moduli space M_{0,n} of marked curves. These bundles arise from data associated to a simple Lie algebra. We will show a correspondence (in certain cases) of the rank of these bundles with coefficients in the cohomology of the Grassmannian. This correspondence allows us to use a formula for computing "quantum Kostka" numbers and explicitly characterize families of bundles of rank one by enumerating Young tableaux. We will show these results and illuminate the methods involved.

** Tuesday, February 14th **

STOCHASTICS/ PROBABILITY SEMINAR

TITLE: A new family of random sup-measures

SPEAKER: Dr. Yizao Wang, University of Cincinnati

TIME: 2:10pm – 3:25pm

ROOM: Ayres 113

A new family of stationary and self-similar random sup-measures are introduced. The representation of this family of random sup-measures is based on intersections of independent stable regenerative sets. These random sup-measures arise in limit theorems for extremes of a family of stationary infinitely divisible processes with long range dependence. The main part of the talk will be devoted to the representation of these random sup-measures. Joint work with Gennady Samorodnitsky.

** Wednesday, February 15th **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: A sharp lower bound estimate for the Green’s function

SPEAKER: Delong Li, UTK

TIME: 1:25pm-2:15pm

ROOM: Ayres 113

In this talk, we obtain a sharp lower bound for the Green’s function on a bounded C^1,1 domain. We will assume a result about the upper bound of Green’s function, and we will prove a lower bound estimate that matches with the upper bound.

ANALYSIS SEMINAR

TITLE: Analytic deformations of commuting squares

SPEAKER: Remus Nicoara, UTK

TIME: 2:30pm-3:20pm

ROOM: Ayres 113

Finite groups, and more generally finite dimensional Hopf C*-algebras, can be encoded in S.Popa’s commuting squares and thus used as construction data for V.Jones’ subfactors. We construct analytic deformations of such commuting squares, and present consequences to the theory of complex Hadamard matrices and the theory of subfactors.

COMPUTATIONAL and APPLIED MATH SEMINAR

TITLE: Fractional partial differential equations: modeling, numerical method, and analysis

SPEAKER: Professor Hong Wang, University of South Carolina

TIME: 3:35pm-4:35pm

ROOM: Ayres 113

Fractional partial differential equations (FPDEs) provide an accurate description of transport processes from many applications, which exhibit anomalous diffusion and long-range spatial interaction and time memory. However, FPDEs raise mathematical and numerical difficulties that have not been encountered in the context of integer-order PDEs. Computationally, because of the nonlocal property of fractional differential operators, the numerical methods for FPDEs often generate dense coefficient matrices for which traditional direct solvers were used that have a computational complexity of O(N3) per time step and memory requirement of O(N2 ) where N is the number of unknowns. This makes numerical simulation of three-dimensional FPDE modeling computationally very expensive. Mathematically, FPDEs exhibit mathematical properties that have fundamental differences from those of integer-order PDEs. We will go over the development of fast numerical methods for FPDEs, by exploring the structure of the coefficient matrices. These methods have approximately linear computational complexity per time step and optimal memory requirement. We will discuss mathematical issues on FPDEs such as wellposedness and regularity of the problems and their impact on the convergence behavior of numerical methods.

** Friday, February 17th **

SPECIAL CAM SEMINAR

TITLE: A Parallel Computational Model for 3D Thermo-Mechanical Stokes Flow Simulations of Ice Sheets

SPEAKER: Professor Lili Ju, University of South Carolina

TIME: 2:00pm-3:00pm

ROOM: Ayres 405

In this talk, we present our work on the development of a parallel three-dimensional, thermo-mechanically coupled, nonlinear Stokes flow computational model "FELIX-S" for ice sheet simulations. Our model features stable and high-order accurate discretizations on variable resolution grids and efficient parallel solution techniques. In particular, we employ a stable and locally mass-conserved finite element approximation for the Stokes problem, an efficient iterative solution method for treating nonlinearity of the viscosity, an accurate finite element solver for the temperature equation, and a conservative finite volume solver for handling change of ice thickness. We also demonstrate efficiency and physical reliability of the Stokes ice flow model using various numerical tests including manufactured solutions, benchmark experiments and the realistic Greenland ice sheet.

COLLOQUIUM

TITLE: Some selection problems in the theory of viscosity solutions.

SPEAKER: Hung Tran, University of Wisconsin–Madison

TIME: 3:40pm-4:30pm

ROOM: Ayres 405

I will explain some interesting selection problems in nonlinear PDEs. The basic question is about how to select one good solution out of many reasonable ones. A question of this type led to the whole theory of viscosity solutions in 1980s. Then I will focus on the vanishing discount problem and describe the main results, which solve an open question also in 1980s. This is a joint work with Ishii and Mitake.

*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:**

Winter Break