Seminars and Colloquiums for the week of October 17, 2016

SPEAKER:

Thomas Weighill, UTK, Monday
Tyler Poppenwimer, UTK, Monday
Math Graduate Student Career Panel, Tuesday
Jay Ver Hoef, National Marine Mammal Lab of the National Oceanic and Atmospheric Association (NOAA), U.S. Dept. of Commerce, Tuesday
David Horton, UTK, Wednesday
Zhenlin Guo, UC Irvine, Wednesday (moved to Thursday)
Kevin Sonnanburg, UTK, Thursday
Nick Dexter, UTK, Friday

TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday (cancelled due to colloquium), & Wednesday
Room: Ayres 401

Hosted by: James Ren & Tamara Riggs

Monday, October 17th

TOPOLOGY/GEOMETRY SEMINAR
TITLE: Montone-light factorizations in coarse geometry
SPEAKER: Thomas Weighill, UTK
TIME: 2:30pm – 3:20pm
ROOM: Ayres 114
Given a continuous map f between topological spaces there are many possible natural factorizations f = gh of f into two continuous maps g and h. For example, one can factorize f as a surjective map followed by an embedding or as a quotient map followed by an injective map. If f is a map between compact Hausdorff spaces, one can also factorize f as a monotone map (a map whose fibres are connected) followed by a light map (a map whose fibres are totally disconnected). Each of these factorizations also satisfies a universal property which can be stated in the category of topological spaces and continuous maps. In this talk, we introduce analogues of topological monotone and light maps in the context of large-scale spaces (where topologically continuous maps are replaced by large-scale continuous, or bornologous, maps), which we call coarsely monotone and coarsely light maps respectively. We will recall the categorical definition of a factorization system before proving that coarsely monotone and coarse light maps are an example of such a system, so that in particular every large-scale continuous map admits a factorization into a coarsely monotone map followed by a coarsely light map. This talk is based on joint work with Jerzy Dydak.

MATH BIOLOGY SEMINAR
TITLE: User’s Guide to Integrodifference Equations
SPEAKER: Tyler Popperwimer, UTK
TIME: 2:30pm – 3:20pm
ROOM: Ayres G003

Tuesday, October 18th

SPECIAL COLLOQUIUM
TITLE: Marcinkiewicz Strong Law of large Numbers and Stochastic Processes/Approximation under Heavy-tailed and Long-range Dependent Setting
TIME: 3:35pm - 4:30pm
ROOM: Ayres 405
Classical time-series theories are mainly concerned with the statistical analysis of light-tailed and short-range dependent stationary linear processes. Applications in network theory and financial mathematics lead us to consider time series models with heavy tails and long memory. Heavy-tailed data exhibits frequent extremes and infinite variance, while positively-correlated long memory data displays great serial momentum or inertia. Heavy-tailed data with long-range dependence has been observed in a plethora of empirical data set over the last fifty years and so. In this study, methodological and theoretical results as well as a considerable portion of applied work address long-range dependence and heavy-tailed types of the data.

The first part of this talk is about development of Marcinkiewicz strong law of large numbers for outer products of multivariate linear processes while handling long-range dependent and heavy-tailed data structure. This result can be applied to obtain Marcinkiewicz strong law of large numbers for non-linear function of partial sums, sample auto-covariances and linear processes in a stochastic approximation setting.

The next part is on developing almost sure convergence rates for linear stochastic approximation algorithms under some assumptions that are implied by Marcinkiewicz strong law of large numbers. Results are verified experimentally in the stochastic approximation setting while handling all gains, long-range dependence and heavy tails and addressing the optimal polynomial rate of convergence by establishing results akin to the Marcinkiewicz strong law of large numbers.

TIME: 3:30pm - 4:30pm
ROOM: Ayres 112
The following former UT math graduate students will be returning to share their experiences and advice:
* Ernest Jum, Senior Quantitative Analyst at BB&T Bank in Winston-Salem, NC
* Mike Kelly, Assistant Professor at Transylvania University, former postdoc at Ohio State University
* Jenny Sinclair, Associate Professor at Georgia Gwinnett College

NIMBioS INTERDISCIPLIMARY SEMINAR
TITLE: Modern spatial statistics: Basis functions, convolutions, and big data
SPEAKER: Jay Ver Hoef, National Marine Mammal Lab of the National Oceanic and Atmospheric Association (NOAA), U.S. Dept. of Commerce
TIME: 3:30pm
ROOM: Hallam Auditorium, Room 206, NIMBioS, Claxton Education Building, 1122 Volunteer Blvd.
Since inception, spatial statistics has been plagued by computational constraints. The central problem is inversion of the covariance matrix, which is an n-cubed problem, which is only compounded by the increased interest in Bayesian hierarchical models that use Markov chain Monte Carlo methods. I will describe a popular trend lately to reparameterize spatial models as linear mixed models where the random-effects design matrix is reduced rank and composed of basic functions. There are interesting connections to spline models and moving average approaches (convolutions) that integrate kernels over white noise. The spatial basis approach allows implementation of models for large data sets and for developing dependence structures for complex topologies. I recount how these approaches became popular from early developments by Barry and Ver Hoef (1996), Higdon (1998), and Wikle and Cressie (1999). I illustrate the new methods with two cases: developing spatial abundance models for count data, and novel spatial models for data collected from stream networks.
Jay Ver Hoef is a statistician for the National Marine Mammal Lab of the National Oceanic and Atmospheric Association, U.S. Department of Commerce. Ver Hoef develops statistical methods and consults on a wide variety of topics related to marine mammals. Ver Hoef’s main statistical interests are in spatial statistics and Bayesian statistics, especially applied to ecological and environmental data.

This seminar will be live streamed. Visit http://www.nimbios.org/videos/livestream for more information and join the conversation on Twitter using #nimbios

Wednesday, October 19th

ANALYSIS SEMINAR
TITLE: A Rough Approach to the Loewner Trace
SPEAKER: David Horton, UTK
TIME: 2:30pm - 3:20pm
ROOM: Ayres 003
We'll take a look at the trace of the Loewner Equation. Specifically, we'll see some results of Friz and Shekhar and discuss how they use rough path theory to show the existence of the trace.

Thursday, October 20th

DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Continuity of Singular Time for Mean-Convex Mean Curvature Flow
SPEAKER: Kevin Sonnanburg, UTK
TIME: 2:00pm – 3:00pm
ROOM: Ayres 112
Mean curvature flow is a parabolic PDE applied to a hypersurface in which each point moves with velocity equal to its mean curvature vector. Under this flow, a compact, mean-convex hypersurface move inward and become singular in finite time. In studying such singularities, considerable work has been done to understand the geometry of their blow-ups. However, there are fewer results regarding stability. I will describe results I have showing continuity of first singular time with respect to initial data, for certain classes of hypersurfaces, and an example of its utility.

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR
TITLE: A Mass Conservative Multi-Level Finite Difference Multigrid Solver
SPEAKER: Zhenlin Guo, UC, Irvine
TIME: 3:35pm – 4:35pm
ROOM: Ayres 405
In this talk, I will present an exactly mass conservative multigrid finite difference method on locally Cartesian, non-uniform meshes. The novelty of the solver is the way in which the mass conservation is seemlessly integrated with the multigrid iterative method, which is based on the adaptive full approximation storage (AFAS) approach. A simple linear interpolation together with the corresponding flux balancing formula are used to match the solution along the coarse-fine grid interfaces. Numerical tests are presented that confirm the mass conservative property, the overall second order accuracy of the method, and the efficiency of the solver.

Friday, October 21st

ORAL SPECIALTY EXAM
SPEAKER: Nick Dexter, UTK
TIME: 12:30pm
ROOM: Ayres 404
His committee consist of Professors: Webster (chair), Karakashian, Salgado, and Wise.

COLLOQUIUM
TITLE: Finite Element Approximation of the Isaacs Equation
TIME: 3:35pm-4:35pm
ROOM: Ayres 405
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size $h$ whereas the coarse scale $\varepsilon$ is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical solution to the viscosity solution as $\varepsilon, h\to0$, and $\varepsilon \gtrsim h^{1/2}|\log h|$. In addition, using a discrete Alexandrov Bakelman Pucci estimate we deduce rates of convergence, under suitable smoothness assumptions on the exact solution.

Joint work with Wujun Zhang (Rutgers)

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:

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: May 2018

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu

The flagship campus of the University of Tennessee System and partner in the Tennessee Transfer Pathway.