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Seminars and Colloquiums
for the week of September 3, 2018


Shandelle Henson, Andrews University
Vasileios Maroulas, University of Tennessee
Giuseppe Tinaglia, King’s College London
Luis Melara, Shippensburg University
Jimmy Scott, University of Tennessee
Mariana Smit Vega Garcia, University of Washington

Lou Gross and Suzanne Lenhart, University of Tennessee
Vivian Healey, University of Chicago

3:00 PM – 3:30 PM
Tuesday & Wednesday (no Monday)
Room: Ayres 401
Hosted by: Hannah Thompson
Topics: Meet & greet with all participants from the Math Department/introductions with new students; How returning graduate students and faculty can best support new graduate students.

Tuesday, 9/4

TITLE: Informal chat with Dr. Shandelle Henson, Professor of Mathematics and Ecology
SPEAKER: Shandelle Henson, Andrews University
TIME: 12:30 PM-1:00 PM
ROOM: Ayres 401 will be provided!

TITLE: Distributions of persistence diagrams
SPEAKER: Vasileios Maroulas, University of Tennessee
TIME: 2:10-3:10
ROOM: A113
I will talk on how we construct probability distributions for persistence diagrams, a toplogical summary. Based on the construction, I will approximate the distributions with a kernel density estimate. Convergence results and simulations will be discussed.

TITLE: Introduction to the Colding-Minicozzi theory
SPEAKER: Giuseppe Tinaglia, King’s College London
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
We will give an overview of the Colding Minicozzi theory for embedded minimal disks.

Wednesday, 9/5

TITLE: Informal Chat with Dr. Luis Melara
SPEAKER: Luis Melara, Shippensburg University
TIME: 12:20 PM-1:00 PM
ROOM: Min H. Kao Building, Room 435
The UT Student Chapter of Society for Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS) invites you to join Dr. Luis Melara for a lecture on mathematics, diversity, and career path. Dr. Melara is an Associate Professor of Mathematics at Shippensburg University. His work intersects the areas of computational science, mathematics, and statistics. As an active member of SACNAS, SIAM, and ACM Tapia Conference, Dr. Melara advocates for making STEM accessible to all students.

TITLE: A Characterization of Vector-Valued Function Spaces Which Characterize Differentiability Properties – Part II
SPEAKER: Jimmy Scott, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
In this series of talks we prove an equivalence of two optically different classes of function spaces. We show that a class of spaces of vector fields whose semi-norms involve the magnitude of “directional” difference quotients is in fact equivalent to the class of fractional Sobolev spaces. The equivalence results from a new “fractional Korn’s inequality.” To further investigate this equivalence, we examine the finer structure of these new function spaces via an analogue of the auxiliary g-function.

In Part I we stated the main results and discussed the proof of the classical Korn’s inequality. In Part II we give the necessary background on singular integrals and sketch the proof of the fractional Korn’s inequality.

Thursday, 9/6

TITLE: Recent developments in the thin obstacle problem
SPEAKER: Mariana Smit Vega Garcia, University of Washington
TIME: 4:00 PM-5:00 PM
ROOM: Ayres 121
The study of the classical obstacle problem began in the 60's with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades it has led to beautiful and deep developments in calculus of variations and geometric partial differential equations. One of its crowning achievements has been the development, due to L. Caffarelli, of the theory of free boundaries. Nowadays the obstacle problem continues to offer many challenges and its study is as active as ever. In particular, over the past years there has been some interesting progress the thin obstacle problem, also called Signorini problem.

In this talk I will overview the thin obstacle problem for a divergence form elliptic operator, and describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the free boundary, in particular the regular and singular sets. The proofs are based on Almgren, Weiss and Monneau type monotonicity formulas. This is joint work with Nicola Garofalo and Arshak Petrosyan.

Friday, 9/7

TOPIC: Regime Shifts in Ecosystems
LEADERS: Lou Gross and Suzanne Lenhart, University of Tennessee
TIME: 10:10 AM-11:00 AM
ROOM: Ayres 401

TITLE: Scaling Limits and the Loewner Equation: From SLE to Tree Embedding
SPEAKER: Vivian Healey, University of Chicago
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
Starting with a simple random walk, rescale (in space and time) and take the limit as the step size goes to zero; the result is Brownian motion. But what limit would you get if you started by assuming that the random walk never intersected itself? The answer (to many versions of this question in two dimensions) is Schramm-Loewner evolution (SLE). In this talk, we will discuss SLE as both the scaling limit of discrete processes (like the loop-erased random walk) and as the continuous time output of the Loewner equation when Brownian motion is used as the equation’s input, or “driving function.” However, the Loewner equation can be used to generate more than curves. In the second half of the talk, we will describe recent work that uses the Loewner equation to embed trees in the upper half-plane, and we will investigate the scaling limit of this process. (Joint work with Govind Menon, Brown University.)

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:

Aug. 27, 2018



last updated: September 2018

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