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Seminars and Colloquiums
for the week of April 9, 2018


SIAM Chapter Meeting - Dr. Patrick Shipman, Colorado State University
Pawel Grzegrzolka, University of Tennessee
Hai Long Dao, University of Kansas
Solesne Bourguin, Boston University
Patrick Shipman, Colorado State University
Henri Roesch, University of California, Irvine
Joseph Daws, University of Tennessee
Jin Wang, University of Tennessee, Chattanooga
Abbas Momeni, Carleton University
Farzana Nasrin, Texas Tech University
Anne Ho, University of Tennessee
Mat Langford, University of Tennessee
Colloquium - Patrick Shipman, Colorado State University

3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Cassie Micucci

Monday, April 9

TITLE: Meet and greet with Dr. Patrick Shipman from Colorado State University
TIME: 12:20 PM-1:00 PM
ROOM: Ayres 401
Lunch will be served.

TITLE: Coarse Proximity
SPEAKER: Pawel Grzegrzolka, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 112
The idea of “translating” a small-scale world to its large-scale counterpart has been extensively explored by coarse topologists. Uniform spaces and surroundings introduced by Weil and Bourbaki were translated to the large-scale world by Roe in terms of coarse structures and controlled sets. Tukey presented a covering definition of a uniform space which inspired Dydak and Hoffland to introduce large scale structures - a covering approach to coarse spaces. Recently, there have been other attempts to translate results from the small-scale world to its large-scale counterpart, including “coarsening” the notion of proximity (see for example the work of Kalantari and Honari).

In this talk, we will review the notion of a proximity space and introduce the definition of a metric coarse proximity. After investigating a few properties of this relation, we will generalize the metric case to obtain coarse proximities on any set with bornology. We will show that coarse proximity relations induce an equivalence relation on the power set of a given space, and consequently that every coarse proximity space induces a coarse space. We will conclude with the existence of the category of coarse proximity spaces whose morphisms are closeness classes of coarse proximity maps. This is joint work in progress with Jeremy Siegert.

TITLE: On h-vector of standard graded algebras
SPEAKER: Hai Long Dao, University of Kansas
TIME: 3:35 PM-4:25 PM
ROOM: Ayres 112
Let R be a standard graded algebra over an algebraically closed field. The h-vector of R is the coefficients vector of the numerator of the (reduced) Hilbert series of R. These numbers have been studied extensively in algebraic geometry, commutative algebra and combinatorics. For example, It is a classical and easy result that if R is Cohen-Macaulay, then the h-vector is non-negative. This talk will focus on recent results about how the singularities of R affect the size and shapes of the h-vectors. If time permits, a surprising connection to how the topology of a hyperplane section of R can behave will be described. Based on joint work with Linquan Ma and Matteo Varbaro.

Tuesday, April 10

TITLE: Four moments theorems on Markov chaos
SPEAKER: Solesne Bourguin, Boston University
TIME: 2:10 PM-3:20 PM
ROOM: Ayres 114
In this talk, we show how to use the Markov diffusion generator framework introduced by Ledoux in order to obtain limit theorems for the approximation of invariant measures of diffusions, where a sufficient condition for convergence is given in terms of a finite linear combination of moments. We will illustrate these results for the Pearson class of probability measures, and recover classical results as particular cases.

TITLE: Counterdiffusion in Biological and Atmospheric Systems
SPEAKER: Patrick Shipman, Colorado State University
TIME: 3:30 PM-4:30 PM; arrive early for cookies, coffee, and tea
ROOM: Claxton 206
In topochemically organized, nanoparticulate experimental systems, vapor diffuses and convects to form spatially defined reaction zones. In these zones, a complex sequence of catalyzed proton-transfer, nucleation, growth, aggregation, hydration, charging processes, and turbulence produce rings, tubes, spirals, pulsing crystals, oscillating fronts and patterns such as Liesegang rings. We call these beautiful 3-dimensional structures “microtornadoes”, “microstalagtites”, and “microhurricanes” and make progress towards understanding the mechanisms of their formation with the aid of mathematical models.  This analysis carries over to the study of similar structures in protein crystallization experiments and the formation of periodic structures in plants.

Sponsored by our SIAM Student Chapter and by NIMBioS.

TITLE: Isolated Horizons and the Null Penrose Inequality
SPEAKER: Henri Roesch, University of California, Irvine
TIME: 5:00 PM-6:00 PM
ROOM: Ayres 113
In the first half of the talk, we introduce a new quasi-local mass with interesting properties along null flows off of a 2-sphere in spacetime or, equivalently, foliations of a null cone. We also show how certain, fairly generic, convexity assumptions on the null cone allows for a proof of the Null Penrose Inequality. On the Black Hole Horizon, we find that the convexity assumptions become sharp; therefore, the second half of the talk will explore the existence of a class of Black Hole Horizons admitting such convexity. From this, building upon the work of S. Alexakis, we will show that the Schwarzschild Null Cone--the case of equality for the Penrose Inequality--is also stable under small metric perturbations. 

Wednesday, April 11

TITLE: Compressed sensing for image reconstruction with wavelets
SPEAKER: Joseph Daws, University of Tennessee
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 112
We propose a compressed sensing approach for the reconstruction of functions or images represented by their expansion in a wavelet basis, from only a small number of samples. The success of applying wavelet representations for image reconstruction and compression has inspired many sparse recovery techniques. However, these approaches can be improved by exploiting the fact that the support of the coefficients of functions sparse in a wavelet basis lie on or nearly on a binary tree.

In particular, we show that the important wavelet coefficients for a certain class of functions and images are concentrated on a downward closed tree, and present a weighted $\ell_1$ minimization strategy to recover these coefficients. Following some of the results of Chkifa, Dexter, Tran, and Webster on compressed sensing for the approximation of high-dimensional functions, we also present theoretical estimates related to the sampling complexity of our scheme as compared to unweighted $\ell_1$ minimization. Several numerical examples are provided to show the effectiveness of this weighted $\ell_1$ minimization scheme for solving the image inpainting problem.

Thursday, April 12

TITLE: Cholera modeling: bacterial dynamics, outbreak simulation, and impact of awareness programs
SPEAKER: Jin Wang, University of Tennessee at Chattanooga
TIME: 11:10 AM-12:00 PM; pizza will be served
ROOM: NIMBioS, Claxton 105
We present some recent work in the mathematical modeling of cholera, a severe waterborne infection caused by the bacterium Vibrio cholerae. We show that the intrinsic bacterial dynamics may play an important role in the transmission and spread of the disease. We demonstrate that education and awareness programs can have significant impact on the development of a cholera outbreak, though different mathematical models may yield qualitatively different dynamical behaviors. Our work underscores the importance of validating key modeling assumptions and connecting models with realistic data. In addition, we present some results in the modeling and simulation of cholera outbreaks in the real world.

TITLE: Smoothing Splines on Ball domains with Applications to Optometry and Ophthalmology
SPEAKER: Farzana Nasrin, Texas Tech University
TIME: 11:10 - 12:10 PM
ROOM: Ayres 111
The identification of metrics to correctly diagnose corneal ectatic diseases, designing customized lenses with aspherical back surfaces for patients with corneal ectasia, and screening for refractive surgery are of great interest in ophthalmology and optometry. A precise understanding of the shape of the cornea is necessary to address all of these important problems. We develop a novel algorithm to reconstruct the shape of the cornea using data from advanced medical imaging devices such as Anterior Segment Optical Coherence Tomographer or Scheimpug imager. We cast the problem as the construction of smoothing splines on non-rectangular domains and develop an algorithm to compute the smoothing spline from noisy data that is optimal in the sense of generalized cross validation. This algorithm provides new and powerful tool for the simultaneous computation of diagnostic parameters for corneas such as anterior and posterior elevation, pachymetry, and true mean curvature maps from the data on non-rectangular grid. Our another novel contribution is the computation of the true mean curvature over every point of a central region of the cornea. We find that a different combination of metrics is useful for the diagnosis of existing ectasia (true mean curvature and anterior elevation map) as opposed to subclinical ectasia (pachymetry and posterior elevation map) by applying our method on different types of corneas. The former is useful for contact lens design, while the latter is useful for screening of patients for refractive surgery.

TITLE: A new variational principle with applications in partial differential equations and Analysis
SPEAKER: Abbas Momeni, Carleton University
TIME: 2:00 PM-3:10 PM
ROOM: Ayres 114
In a wide range of mathematical problems the existence of a solution is equivalent to the existence of a fixed point for a suitable map or a critical point for an appropriate variational or hemi-variational problem. In particular, in real life applications we are interested in finding such solutions which possesses certain properties. The existence theory is therefore of paramount importance in several areas of mathematics and other sciences. In this talk we shall provide a variational principle that allows us to study problems of the general form F(u)=0 on a given convex set K. 

This variational principle has many applications in partial differential equations while unifying and generalizing several results in nonlinear Analysis such as some fixed point theorems, critical point theory on convex sets and the principle of symmetric criticality.

SPEAKER: Anne Ho, University of Tennessee
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
This talk is about secret messages, hackers, Julius Caesar, the FBI, data breaches, number theory, and puzzles.  Your first puzzle is the title of this talk.  During the presentation, we will discuss more puzzles, historical ciphers, and relevant current events.

TITLE: Local convexity estimates for mean curvature flow.
SPEAKER: Mat Langford, University of Tennessee
TIME: 5:05 PM-6:05 PM
ROOM: Ayres 113
I will present local convexity estimates for mean curvature flow and discuss some possible applications. The estimate is proved by localizing the Stampacchia iteration argument of Huisken and Huisken—Sinestrari.

Friday, April 13

TITLE: Conformal parameterizations of Euclidean, timelike, and spacelike surfaces 
SPEAKER: Patrick Shipman, Colorado State University
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
Abstract: The complex-analytic approach to constructing minimal surfaces carried out by Weierstrass and Enneper has since been extended to create conformal parameterizations of minimal surfaces, surfaces of constant mean curvature, and more general surfaces in Euclidean and Lorentz spaces.  The talk will begin with an exposition of generalized Weierstrass-Enneper representations, and we will find a Lie-Algebraic formulation that unites the representations in various spaces into one coherent framework.  Surfaces in Lorentz spaces can be classified as timelike or spacelike.   The second part of the talk will focus on timelike surfaces and their relation to Lorentz-conformal transformations in the plane.  Lorentz-conformal transformations in the plane are holomorphic with respect to a hyperbolic structure on the plane and satisfy the wave equation.

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:




3_12_18 (spring break)

























last updated: May 2018

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