Seminars and Colloquiums
for the week of August 31, 2015
Eddie Tu, Tuesday
Xiaobing Feng, Wednesday
Tuoc Phan, Thursday
Chelsea Lewis, Friday
Andrew Starnes, Friday
Vasileios Maroulas, Friday
Tuesday, September 1
TITLE: The probabilistic symbol for continuous-time Markov processes
ROOM: Ayres 112
SPEAKER: Eddie Tu, UTK
ABSTRACT: Various analytic tools can be used to study the behavior of and to generate continuous-time Markov processes. In this talk, we will carefully develop such tools, in particular, the pseudo-differential operator and its symbol, and discuss the roles of these concepts in understanding and analyzing Markov processes.
Wednesday, September 2
TITLE: Finite Element Methods for Non-divergence Form Elliptic PDEs with Applications to Stochastic Optimal Control
ROOM: Ayres 110
SPEAKER: Xiaobing Feng, UTK
Abstract: This talk will present some recent developments in finite element methods for approximating strong solutions for a class of linear elliptic PDEs in non-divergence form whose leading coefficients are only continuous. Such PDEs are building blocks of fully nonlinear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control and financial mathematics. The focus of the talk will be on presenting some newly developed C^0 (and L^2) discontinuous Galerkin finite element methods, which are simple to implement and can be done using standard finite element codes. The convergence analysis and error estimates of these methods call for establishing a finite element discrete Calderon-Zygmund theory which will be highlighted in the talk.
Thursday, September 3
TITLE: Local gradient estimates for solutions of parabolic equations with Divergence-free drifts
ROOM: Ayres 114
SPEAKER: Tuoc Phan, UTK
Abstract: We investigate the regularity of weak solutions of Non-homogeneous parabolic equations with divergence-free drifts. Assuming that the drifts satisfy some mind regularity conditions, we establish locally $L^p$-estimates for the gradients of weak solutions. Our results are generalized to parabolic equations in divergence form with elliptic symmetric part, and a skew-symmetric part. Our main theorem only requires the oscillation of the symmetric part to be sufficiently small, while neither the boundedness nor the smallness on the oscillation is imposed on the skew-symmetric part. The results therefore significantly improve many known results in literature.
Friday, September 4
TITLE: Invasion of Alien Species
SPEAKER: Chelsea Lewis, UTK
Abstract: Chapter 2 from Shigesada and Kawasaki book on Biological Invasions.
TITLE: An Introduction to Loewner Equation
ROOM: BU 476
SPEAKER: Andrew Starnes, UTK
Abstract: The Loewner equation was an important tool in proving the Bieberbach conjecture and in the creation of the Schramm-Loewner Evolution (SLE). This talk introduce the Loewner equation as well as some of its uses, properties, and different forms. We will conclude the talk by mentioning a conjecture about the multi-slit Loewner equation, which will be discussed in the following talk next week.
TITLE: Navigating the Stochastic Filtering Landscape
ROOM: Ayres 405
SPEAKER: Vasileios Maroulas, UTK
Abstract: This talk navigates us through the landscape of stochastic filtering, its computational implementations and their applications in science, engineering and national defense. We start by exploring properties of the optimal filtering distribution. Unfortunately, under general conditions, the filtering distribution does not enjoy a closed form solution. Employing several methods, e.g. particle filters, we approximate it and we explore properties of the underlying process and its engaging parameters. The parameter estimation leads us to a research path which involves a novel algorithm of particle filters blended with a Markov Chain Monte Carlo scheme, a sequential Empirical Bayes method and related sufficient estimators. Last stop of this talk is at the Fukushima power plant station whose data we use in order to estimate the spatiotemporal evolution of radioactive material caused by the disastrous accident in the region in 2011.
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