Seminars and Colloquiums
for the week of March 26, 2018
Jerzy Dydak, University of Tennessee
Xiaoyang Pan, University of Tennessee
Mathew Langford, University of Tennessee
Andreas Prohl, Universität Tübingen, Germany
Athmanath Senthilnathan, University of Tennessee
Marie Jameson, University of Tennessee
Martin Reiris, Universidad de la Rep˙blica, Uruguay
3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Alec Lewald and Liam Bitting
Monday, March 26
TOPOLOGY/ GEOMETRY SEMINAR
Title: Unifying large scale and small scale
Speaker: Jerzy Dydak, University of Tennessee
Time: 2:30 PM-3:20 PM
Room: Ayres 112
I will discuss a structure that unifies small scale (uniform and proximity spaces) with large scale (coarse spaces). It is an orthogonality relation that leads naturally to parallelism. In particular, Euclidean lines are classically parallel if and only if they are parallel in the more general sense.
Tuesday, March 27
Title: Asymptotics for the optimal filter of nonlinear dynamical systems driven by Levy noise
Speaker: Xiaoyang Pan, University of Tennessee
Time: 2:10 PM-3:20 PM
Room: Ayres 114
In this talk, we focus on the asymptotic behavior of the optimal filter where both signal and observation processes are driven by Levy noises. Indeed, we study large deviations for the case where the signal-to-noise ratio is small by considering weak convergence arguments. To that end, we first prove the uniqueness of the solution of the controlled Zakai and Kushner-Stratonovich equations. For this, we employ a method which transforms the associated equations into SDEs in an appropriate Hilbert space. Next, taking into account the controlled analogue of Zakai and KushnerStratonovich equations, respectively, the large deviation principle follows by employing the existence, uniqueness and tightness of the solutions. This is a joint work with Vasileios Maroulas and Jie Xiong.
GENERAL RELATIVITY SEMINAR
Title: The reduction of the positive mass theorem to Lohkamp’s "no positive scalar curvature islands” Theorem.
Speaker: Mathew Langford, University of Tennessee
Time: 5:00 PM-6:00 PM
Room: Ayres 113
We begin reading the recent preprint of Schoen and Yau by reducing the positive mass theorem to Lohkamp’s "no positive scalar curvature islands” Theorem (which states that the connected sum of a closed, oriented $n\geq 3$-manifold with an $n$-torus cannot admit a positive scalar curvature metric).
Wednesday, March 28
COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
Title: Stochastic optimal control in Ferromagnetism
Speaker: Andreas Prohl, Universität Tübingen, Germany
Time: 3:35 PM-4:35 PM
Room: Ayres 112
The stochastic Landau-Lifshitz-Gilbert equation is a stochastic PDE which describes the domain wall motion in nanomagnets in the presence of thermal fluctuations. In this talk I will present a related optimal control problem to control domain wall motion, and prove its solvability. The convergence of a finite element approximation of the problem is shown in space-dimension one, which then allows to apply Pontryagin's maximum principle for this finite dimensional setting; then, the resulting coupled system of forward-backward SDEs is numerically solved by means of the stochastic gradient method to enable practical simulations. If time permits, I will also briefly discuss the alternative dynamic programming approach where solving the high-dimensional Hamilton-Jacobi-Bellman equation is a central issue. - This is joint work with T. Dunst, A.K. Majee, C. Schellnegger (U Tuebingen), G. Vallet (U Pau), and M. Jensen (U Sussex).
Thursday, March 29
MATH BIOLOGY SEMINAR
Title: Evolutionary learning of adaptation to varying environments through a transgenerational feedback
Speaker: Athmanath Senthilnathan, University of Tennessee
Time: 11:10 AM-12:00 PM
Room: Hesler 427
Title: Adding and counting: as easy as 1, 2, 3…
Speaker: Marie Jameson, University of Tennessee
Time: 3:40 PM-4:35 PM
Room: Ayres 405
In this talk, we’ll dive into the theory of “integer partitions,” which are combinatorial objects that are very easy to define: a partition of a positive integer n is just a way of writing n as a sum of positive integers. Although partitions are simple to define, it turns out that they have very surprising properties and far-reaching connections to other areas of study.
GEOMETRIC ANALYSIS SEMINAR
Title: Bakry-Émery geometric comparison techniques and applications to general relativity (a more detailed account)
Speaker: Martin Reiris, Universidad de la República, Uruguay
Time: 5:00 PM-6:00 PM
Room: Ayres 113
Starting with the work of Bakry, Émery, Ledoux, and others on diffusion processes on Riemannian manifolds, several novel Riemannian-comparison techniques with broad applications have been developed over the last decades. Classical theorems, like Myer's compactness or Cheeger-Gromoll's splitting were generalised and impressive applications were found by Perelman in the Ricci flow and soliton's theory. In this talk I will begin reviewing the probabilistic origins of such techniques, introduce then some basic theorems, and finally show applications to a wide range of problems related to static and stationary solutions of the Einstein equations (the 'solitons' of the theory) with or without matter. Open problems and prospective directions of work will be mentioned.
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
3_12_18 (spring break)