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Seminars and Colloquiums
for the week of October 1, 2018


Nikolay Brodskiy, University of Tennessee
Madeline Locus Dawsey, Emory University
Jan Rosinski, University of Tennessee
Theodora Bourni, University of Tennessee
Abner J. Salgado, University of Tennessee

3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Rooms: Ayres 401
Hosted by: Anne Ho & Christina Edholm
Topics: How to have conversations with faculty members while searching for an advisor; things to expect for an oral exam; tips for dissertation writing.

Monday, 10/1

TITLE: Dimension of tree-graded spaces
SPEAKER: Nikolay Brodskiy, University of Tennessee
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 406
The concept of tree-graded space was introduced by C. Drutu and M. Sapir when they proved (jointly with D. Osin) that a finitely generated group G is relatively hyperbolic with respect to finitely generated subgroups H1, . . . , Hn if and only if every asymptotic cone of G is tree-graded with respect to the limits of sequences of cosets of the subgroups Hi. We will explore how various dimension-like properties of a tree-graded space can be derived from the corresponding properties of the building pieces of the space. The talk will be accessible to graduate students.

TITLE: Moonshine for finite groups
SPEAKER: Madeline Locus Dawsey, Emory University
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 113
Weak moonshine for a finite group G is the phenomenon where an infinite dimensional graded G-module (see pdf for formula) has the property that its trace functions, known as McKay-Thompson series, are modular functions.  Recent work of Dehority, Gonzalez, Vafa, and Van Peski established that weak moonshine holds for every finite group.  Since weak moonshine only relies on character tables, which are not isomorphism class invariants, non-isomorphic groups can have the same McKay-Thompson series.  We address this problem by extending weak moonshine to arbitrary width (see pdf).  Namely, for each 1 <_ r <_ s and each irreducible character X_i, we employ Frobenius' r-character extension (see pdf) to define McKay-Thompson series of (see pdf) (r copies) for each r-tuple in (see pdf) (r copies).  These series are modular functions.  We find that complete width 3 weak moonshine always determines a group up to isomorphism.  Furthermore, we establish orthogonality relations for the Frobenius r-characters, which dictate the compatibility of the extension of weak moonshine for V_G to width s weak moonshine.

Tuesday, 10/2

TITLE: Levy systems and moment formulas for mixed type Poisson integrals
SPEAKER: Jan Rosinski, University of Tennessee
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 113
A modern direct approach to calculus of Poisson random measures is based on the configuration space. In this setting we consider the Mecke-Palm formula, an important identity in stochastic analysis of Poisson random measures. We propose its generalization to (multiple) mixed-type Mecke-Palm formula and show that such generalization is useful in the study of Levy systems. This talk is based on a join work with K. Bogdan, G. Serafin, and L. Wojciechowski.

TITLE: Colding-Minicozzi Paper 2-part 4
SPEAKER: Theodora Bourni, University of Tennessee
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
We will show polynomial bounds of the area of embedded minimal disks and that the total curvature over large balls can be bounded by the area. Finally we will show the existence of large 1/2-stable sectors, which is key in proving the local structure near the axis.

Wednesday, 10/3

TITLE: Regularity and rate of approximation for obstacle problems for a class of integro-differential operators
SPEAKER: Abner J. Salgado, University of Tennessee
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 113
We consider obstacle problems for three nonlocal operators:

A) The integral fractional Laplacian
B) The integral fractional Laplacian with drift
C) A second order elliptic operator plus the integral fractional Laplacian

For the solution of the problem in Case A, we derive regularity results in weighted Sobolev spaces, where the weight is a power of the distance to the boundary. For cases B and C we derive, via a Lewy-Stampacchia type argument, regularity results in standard Sobolev spaces. We use these regularity results to derive error estimates for finite element schemes. The error estimates turn out to be optimal in Case A, whereas there is a loss of optimality in cases B and C, depending on the order of the integral operator.


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 mlangfo5 AT utk DOT edu

Past notices:

Sept. 24, 2018

Sept. 17, 2018

Sept. 10, 2018

Sept. 3, 2018

Aug. 27, 2018



last updated: October 2018

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