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Seminars and Colloquiums
for the week of February 26, 2018


Nicolo Zava, University of Udine, Italy
Yu-Ting Chen, University of Tennessee
Michael Frazier, University of Tennessee
Michael Wise, University of Tennessee
Suzanne Lenhart, University of Tennessee
Michael Kirby, Colorado State University
Ryan Unger, University of Tennessee
Michael Kirby, Colorado State University

No Tea Time this week.

Monday, February 26

TITLE: Large-scale topologies and generalizations of coarse spaces
SPEAKER: Nicolo Zava, University of Udine, Italy
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 112
Coarse geometry, the branch of topology that studies the asymptotic behaviour of spaces, was originally developed for metric spaces and then Roe introduced coarse structures. As we can describe many small-scale properties of metric spacesthrough uniformities, we can similarly express a lot of the large-scale ones by means of coarse structures. Moving from the concept of bounded structures, in this talk, we propose a large-scale counterpart of topology, which we call large-scale topology. Moreover, we show some relevant similarities of this theory with general topology and weintroduce some generalizations of coarse spaces (namely, entourage spaces, quasi-coarse spaces and semi-coarse spaces) that are closely related to both large-scale topologies and coarse spaces.

Tuesday, February 27

TITLE: Some techniques for mean-field spin glass models
SPEAKER: Yu-Ting Chen, University of Tennessee
TIME: 2:10 PM-3:20 PM
ROOM: Ayres 114
I will discuss the proof of the Ghirlanda-Guerra identities for the Sherrington-Kirkpatrick model. These are the central identities leading to Panchenkoís unifying method for Parisiís solution of the model during the last decade.

Wednesday, February 28

TITLE: Introduction to Calderon-Zygmund and Littlewood-Paley Theory
SPEAKER: Michael Frazier, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 112
Consider an operator, defined with respect to a given orthonormal system, which multiplies each coefficient of a function in this system by a factor of magnitude at most 1. Such a "coefficient reduction" operator is automatically bounded on L^p for 1 < p < infinity for the wavelet expansion. These operators are not necessarily L^p bounded for the Fourier expansion unless p=2. This L^p stability of the wavelet expansion is an advantage for applications such as signal compression or denoising. The mathematics behind this property of wavelets goes back to the theory of Calderon-Zygmund singular integral operators, but in the vector-valued setting. We will outline this theory today, with the goal in the next lecture of describing its matrix-weighted analogue.

TITLE: Finite Element Methods for a System of Dispersive Equations
SPEAKER: Michael Wise, University of Tennessee
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 112
This talk is concerned with the numerical approximation of periodic solutions of systems of Kortewegñde Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ in their treatment of the third derivative. One approach preserves a certain important invariant of the system while the other, somewhat more standard method introduces a measure of dissipation. For both methods, we prove convergence of a semi-discrete approximation and highlight differences in the basic assumptions required for each. Numerical experiments are presented whose aim is to study the accuracy of the two schemes when integrations are made over long time intervals.

Thursday, March 1

TITLE: Introduction to Control Issues for Linear System of DEs
SPEAKER: Suzanne Lenhart, University of Tennessee
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 114
We discuss the basic concepts of controllability and observability for linear system of ordinary differential equations. A couple of illustrative examples will be given. The notation of feedback control will be presented also.

TITLE: Machine Learning and Optimization Tools for The Analysis of Data from Human and Animal Infectious Disease Challenges
SPEAKER: Michael Kirby, Colorado State University
TIME: 3:30PM-4:30 PM
ROOM: Ayres 405
This talk will focus on new algorithmic approaches for two problems in data science.† First, we consider the extraction of signal from gene expression data sets related to the host immune response to infection.† We observe that signatures of infection appear even†within five hours†of exposure.† Machine learning can rediscover what biologists already know, and maybe more?!† Next we will explore a new algorithm for the modeling of streaming time series and how this can be used for studying mice exposed to salmonella infection.† The core of the algorithm is based on radial basis functions and the dual simplex method.† The approach is viable for high throughput time-series analysis.

TITLE: The isoperimetric problem and spherical rearrangements II
SPEAKER: Ryan Unger, University of Tennessee
TIME: 5:05 PM-6:05 PM
ROOM: Ayres 113
We show how to decrease the Sobolev norm of a smooth function by spherically rearranging its level sets (Polya-Szego inequality). This is connected to the Euclidean isoperimetric problem and the best constant in the Sobolev inequality.

Friday, March 2

TITLE: Some new geometric tools for analyzing data
SPEAKER: Michael Kirby, Colorado State University
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
We shall show some striking examples of geometry in data and how it may be characterized mathematically and understood computationally. We shall introduce the Grassmannian as a means to encode data and illustrate how algorithms for vector spaces, or embedded manifolds, can be extended to the setting of abstract manifolds.† We consider applications to face recognition, hyperspectral imaging and time series analysis. We will finish with an interesting formula that relates the computation of generalized curvatures on sample curves in high dimensions using the singular value decomposition on local regions.

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

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last updated: March 2018

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