**Seminars and Colloquiums**

for the week of September 26, 2016

for the week of September 26, 2016

*SPEAKER:*

Metin Alper Gur, Indiana University, Monday

Yue Zhou, UTK, Monday

Jan Rosinski, UTK, Tuesday

Ken Stephenson, UTK, Wednesday

Katharine Turner, École Polytechnique Fédérale de Lausanne EPFL, Switzerland, Wednesday

3rd New Frontiers in Probability and Applications Lecture - Ramon van Handel, Princeton University, Friday

*TEA TIME
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted By: Kevin Sonnanburg*

**Monday, September 26th **

TOPOLOGY/GEOMETRY SEMINAR

TITLE: Hypersurfaces with central convex cross sections

SPEAKER: Metin Alper Gur, Indiana University

TIME: 2:30pm – 3:20pm

ROOM: Ayres 114

The compact transverse cross-sections of a cylinder over a central ovaloid in R^n (n>2) with hyperplanes are central ovaloids. A similar result holds for quadrics (level sets of quadratic polynomials) in teir compact transverse cross-sections with hyperplanes are ellipsoids, which are central ovaloids. In R^3, Blaschke, Brunn, and Olovjanischniko found results for compact convex surfaces that motivated B. Solomon to prove that these two kinds of example provide the only complete, connected, smooth surfaces in R^3 whose ovaloid cross-sections are central. We generalize that result to all higher dimensions, proving: If M in R^n (n>3) is a complete, connected, smooth hypersurface, which intersects at least one hyperplane transversally along an ovaloid, and every such ovaloid on M is central, then M is either a cylinder over a central ovaloid or a quadric.

MATH BIOLOGY SEMINAR

TITLE: Invasions in a Multispecies System

SPEAKER: Yue Zhou, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres G003

** Tuesday, September 27th **

STOCHASTICS SEMINAR

TITLE: Isomorphism identities for perturbed infinitely divisible processes

SPEAKER: Jan Rosinski, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

We consider infinitely divisible processes perturbed by an additive independent noise. We study admissible perturbations under which the perturbed process, which need not be infinitely divisible, is absolutely continuous with respect to the unperturbed process. The Dynkin's isomorphism theorem is an example of such phenomenon, where the local time of a Markov process is the perturbation.

** Wednesday, September 28th **

ANALYSIS SEMINAR

TITLE: Convergence of Shapes in Conformal Tiling III

SPEAKER: Ken Stephenson, UTK

TIME: 2:30pm-3:20pm

ROOM: Ayres 003

We wrap up the proof of convergence, using the pinwheel tiling as our key example. The last steps involve various limit arguments, sequence extractions, quasiconformal mapping arguments.

SPECIAL COLLOQUIUM

TITLE: Topology meets Neuroscience

SPEAKER: Katharine Turner, École Polytechnique Fédérale de Lausanne EPFL, Switzerland

TIME: 3:35pm-4:35pm

ROOM: Ayres 405

I will present a variety of applications of topology to neuroscience. I will describe collaborations in progress with the Blue Brain Project on topological analysis of the structure and function of digitally reconstructed microconnectomes, and on topological classification of neuron morphological types. I will mention concurrence topology as a way to analyze fMRI data and how we can perform null hypothesis testing with it.

** Friday, September 30th **

COLLOQUIUM -
3rd New Frontiers in Probability and Applications Lecture

TITLE: Isoperimetric games

SPEAKER: Ramon van Handel, Princeton University

TIME: 3:35pm-4:35pm

ROOM: Ayres 405

Every child who has played with soap bubbles observes instinctively that the ball has the smallest surface area among all bodies of equal volume: this was already known (it is said) to Dido, queen of Carthage. The analogous property of Gaussian measures has far-reaching implications for probability and geometry in high dimension. These isoperimetric phenomena have their origin in the remarkable convexity properties of the Lebesgue and Gaussian measures. My aim in this talk is to exhibit an unexpected explanation for these phenomena: they are game-theoretic in nature. In particular, the convexity of Gaussian measures arises as the result of a game between two players who compete for control of a Brownian motion. The connection between isoperimetry, convexity, and games provides new insight in this area and gives rise to novel geometric inequalities.

*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:**