**Seminars and Colloquiums**

for the week of November 20, 2017

for the week of November 20, 2017

*SPEAKERS*

Delong Li, UTK, Monday

Jan Rosinski, UTK, Tuesday

Khoa Dinh/Jeahyun Park, UTK, Wednesday

*TEA TIME*

*3:00 pm – 3:30 pm
Monday, Tuesday,
Wednesday
Ayres 401
Hosted By: Shuler Hopkins*

**Monday, November 20th **

**ORAL EXAMINATION**

TITLE: A formula for the Supersingular polynomial

SPEAKER: Delong Li, UTK

TIME: 3:35pm-4:25pm

ROOM: Ayres 113

In this talk, we will give an explicit formula for the supersingular polynomial. In particular, we will give an elementary proof for the number of supersingular elliptic curves in characteristic p.

**Tuesday, November 21st**

**STOCHASTICS/ PROBABILITY SEMINAR**

TITLE: Strong path-wise approximation of Gaussian and Levy processes, extension of Ito-Nisio theorem, and continuity of Ito map

SPEAKER: Jan Rosinski, UTK

TIME: 2:10-3:25pm

ROOM: Ayres 113

N. Wiener (1923) gave two representations of Brownian motion as random trigonometric series, and showed that these series converge path-wise uniformly. This made Brownian motion a well-defined mathematical object and explained the nature of white noise. Nowadays, such types of series representations are also used to simulate stochastic processes. The mode and type of convergence in the series is crucial when we want to approximate output of a stochastic system (such as the Ito map) by the simulated input. The uniform convergence of the input processes is often insufficient for the convergence of the outputs, which triggered the development of rough path theory. We take a different approach to this problem by extending Ito-Nisio theorem to non-separable function spaces. We apply this approach to show strong path-wise convergence in series expansions of Levy processes, which yields the continuity of Ito map. This talk is based on a joint work with Andreas Basse-O’Connor and Jorgen Hoffmann-Jorgensen of Aarhus University.

**Wednesday, November 22nd **

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR**

TITLE: Morphological Instability in Crystal Growth

SPEAKER: Khoa Dinh, UTK

TIME: 3:35-4:25pm

ROOM: Ayres 113

In this talk, we will introduce Kinetic Monte Carlo method, and show some simulation results of crystal growth by molecular beam epitaxy. We will discuss morphological instability observed in our simulation results.

TITLE: Finite Element Approximation of the p-Laplacian

SPEAKER: Jeahyun Park, UTK

TIME: 3:35-4:25pm

ROOM: Ayres 113

In this talk, I will present the key result from a paper written by John W. Barrett and W. B. Liu, which this presentation is titled after. We will discuss the error bounds of the finite element approximation of the minimization problem derived by the non-homogeneous p-Laplacian equation on a bounded two dimensional domain with a reasonable boundary condition. Though the original paper addresses the case 1?p<2, we will focus on the case p>2, and will impose a few minor restrictions for simplicity.

*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:**