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Seminars and Colloquiums
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:

2_6_17.html

1_30_17.html

1_23_17.html

1_16_17.html

Winter Break

11_28_16.html

11_21_16.html

11_14_16.html

11_7_16.html

10_31_16.html

10_24_16.html

10_17_16.html

10_10_16.html

10_3_16.html

9_26_16.html

9_19_16.html

9_12_15.html

spring_16.html

fall_15.html

 

last updated: February 2017

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