**Seminars and Colloquiums**

for the week of November 27, 2017

for the week of November 27, 2017

*SPEAKERS*

Ken Stephenson, UTK, Wednesday

Jeremy Siegert, UTK, Wednesday

Matthew Dunlop, Caltech, Thursday

Alex Mramor, UC Irvine, Thursday

*TEA TIME*

*3:00 pm – 3:30 pm
Monday, Tuesday, Wednesday
Ayres 401
Hosted By: Cara Sulyok*

**Wednesday, November 29th**

**ANALYSIS SEMINAR**

Title: Emergent Conformal Structure and Computational Extremal Length, Part II

Speaker: Ken Stephenson, UTK

Time: 2:30pm-3:20pm

Room: Ayres 113

I believe that I may have talked about circle packing in the past. I may have mentioned that circle packings impose geometry on abstract combinatorial patterns. I may even have talked about the conformal nature of that geometry. Wouldn't surprise me. It appears, in fact, that that geometry is profoundly "conformal" --- for geometrically random triangulations, conformality seems to emerge spontaneously under the mechanics of circle packing. Humm..., seems I may have talked about that before, too. In any case, now I plan to explain how one can exploit this emergent behavior in practice. The setting is computation of extremal length for data in atmospheric science. The talk will be image-driven and so should be accessible with little background. In addition, it may suggest uses in other areas, whether pure or applied, where geometric surfaces are involved.

**TOPOLOGY/ GEOMETRY SEMINAR**

**Wednesday, November 29th**

**TOPOLOGY/ GEOMETRY SEMINAR**

Title: Deviancy of Coarse Spaces II

Speaker: Jeremy Siegert, UTK

Time: 3:35-4:25pm

Room: Ayres 405

Having defined the basic notions surrounding the deviancy of coarse maps we will briefly review the denominator of deviancy for a close equivalence class of coarse maps. We will then proceed to describe the denominator of deviancy of a particular space X with respect to another space Y which provides a measure of how much X deviates from being coarsely embeddable in Y. This measure turns out to be a coarse invariant of the space X. Throughout this discussion examples in the form of easily understood metric spaces will be provided. Time permitting a generalization of the notions of deviancy to general categories will be described as well as how such notions give rise to ``distances” between invariants in a category and ``topologies” on the objects of categories.

**Thursday, November 30th**

**Mathematical Data Science Seminar**

Title: Dimension robust posterior sampling with non-Gaussian priors

Speaker: Dr. Matthew Dunlop, Caltech

Time: 3:30-4:30pm

Room: Ayres 405

Inverse problems often concern the recovery of a high- or infinite-dimensional state from indirect measurements. Such problems are typically ill-posed, and so require some form of regularization to ensure existence of a unique solution. The Bayesian approach achieves this by quantifying prior beliefs about the solution by a probability distribution, and applying Bayes' rule to construct the posterior distribution. The posterior then contains information about the unknown state and uncertainties associated with it.

Quantities of interest are calculated via integration against the posterior, which numerically requires samples from the posterior. The performance of standard sampling techniques, such as random walk Metropolis, often deteriorates when the dimension of the state space becomes large. Algorithms which possess certain dimension-independent properties are hence of interest. Much theory and methodology exists for dimension robust sampling when Gaussian priors are employed, however in practice it may be more appropriate to have the additional flexibility afforded by hierarchical and non-Gaussian priors. We show how the Gaussian methodology may be utilized in these cases via the use of nonlinear transformations. We illustrate the methodology through numerical examples, including applications in semi-supervised classification, medical imaging and deconvolution.

**GEOMETRIC ANALYSIS SEMINAR**

Title: Applications of mean curvature flow with surgery

Speaker: Alex Mramor, UC Irvine

Time: 5-6pm

Room: Ayres 404

In this talk I will give a brief introduction to the mean curvature flow with surgery and describe some applications of it to studying the moduli space of hypersurfaces and the level set flow.

*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:**