### Seminars and Colloquiums for the week of November 6, 2017

SPEAKERS

Xia Chen, UTK, Tuesday
Andrew Starnes, UTK, Wednesday
Christy Rickett, UTK, Wednesday
Professor Max Jensen, University of Sussex, UK , Wednesday
Igor Verbitsky, University of Missouri, Columbia, Thursday
Ryan Unger, Thursday

TEA TIME
3:00 pm – 3:30 pm
Monday, Tuesday, Wednesday
Ayres 401
Hosted By: Maggie, Cassie, and Kylie

Tuesday, November 7th, 2017

STOCHASTICS/ PROBABILITY SEMINAR
TITLE: Solving Parabolic Anderson with rough and critical Gaussian noise
SPEAKER: Xia Chen (UTK)
TIME: 2:10pm-3:25pm
ROOM: Ayres 113
Abstract: An important class of the parabolic Anderson equations are the ones with Gaussian noise given as the formal derivative of a fractional Brownian sheet. In this talk we consider the cases (1) when the fractional noise has rough components (i.e., the components with Hurster parameters less than half); (2). when the fractional noise produces only local solution.

Some unsolved problems will be mentioned.

Wednesday, November 8th, 2017

ANALYSIS SEMINAR
TITLE: Constant Weights for the Multiple Loewner Equation
SPEAKER: Andrew Starnes, UTK
TIME: 2:30 pm – 3:20pm
ROOM: Ayres 113
Abstract: After a refresher from last week, we pick up where we left off. First, we look more into the multiple Loewner equation (MLE) simulations and show that our controlled oscillation method will converge appropriately. Second, we prove that we can always reduce to the case of constant weights for the MLE. Third, we use this result to show that randomly rotating between driving functions still gives the desired convergence. Finally, if time allows, we will discuss the errors from our random simulations. For slides from last week's talk, email the presenter at starnes@math.utk.edu.

TOPOLOGY/ GEOMETRY SEMINAR
TITLE: An Investigation of Hilbert's $13^{th}$ Problem
SPEAKER: Christy Rickett, UTK
TIME: 3:35 pm – 4:25 pm
ROOM: Ayres 405
Abstract: In the year 1900 at the International Congress of Mathematicians in Paris, David Hilbert famously presented 23 problems as a challenge to mathematicians for the $20^{th}$ century. Hilbert's $13^{th}$ Problem asks whether the root of a general seventh-degree polynomial can be expressed in terms of functions of fewer than three variables. In 1957, Kolmogorov and Arnold provided a solution that yields powerful connections to dimension theory.
\bigbreak

Hilbert's $13^{th}$ Problem was motivated by efforts to eliminate as many coefficients as possible from polynomial equations. By the end of the $19^{th}$ century, various techniques were known for simplifying polynomials by means of Tschirnhaus transformations. In this talk, we will motivate Hilbert's $13^{th}$ Problem by explicitly solving a cubic equation by using a Tschirnhaus Transformation.

COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
TITLE: Dynamic Programming for Finite Ensembles of Nanomagnetic Particles
SPEAKER: Professor Max Jensen, University of Sussex, UK
TIME: 3:35pm-4:25pm
ROOM: Ayres 113
Abstract: The stochastic Landau-Lifshitz-Gilbert equation describes magnetization dynamics in ferromagnetic materials in a thermal bath. In this presentation I discuss the optimal control of a finite spin system governed by the stochastic Landau-Lifshitz-Gilbert equation in order to guide the configuration optimally into a target state. At the heart of our analysis is a Bellman PDE on the state manifold, for which we show wellposedness as well as regularity of the value function and the optimal controls. The seminar is based on joint work with Ananta Majee and Andreas Prohl (University of Tuebingen, Germany).

Thursday, November 9th, 2017

DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Global pointwise estimates and existence theorems for positive solutions to linear and nonlinear elliptic PDE
SPEAKER: Igor Verbitsky, University of Missouri, Columbia
TIME: 2:10pm – 3:10pm
ROOM: Ayres 114
Abstract: Global pointwise estimates of positive solutions and existence theorems will be discussed for elliptic equations of the type -Lu+ Vu^{q}=f, where L is an elliptic operator in divergence form, q belongs to R\{0}, and V is a function which may change sign, in a domain Omega contained in R^n, or in a weighted Riemannian manifold, as well as their non-local analogues. This talk is based on joint work with Michael Frazier and Fedor Nazarov, Alexander Grigor'yan, and Adisak Seesanea.

GEOMETRIC ANALYSIS
TITLE: The Yamabe Problem I
SPEAKER: Ryan Unger, UTK
TIME: 5:00 – 6:00pm
ROOM: Ayres 113
Abstract: We will continue our discussion of the resolution of the Yamabe conjecture in the case when the Yamabe energy is positive.

#### 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:

10_30_17.html

10_23_17.html

10_16_17.html

10_9_17.html

10_2_17.html

9_25_17.html

9_18_17.html

9_11_17.html

9_4_17.html

8_28_17.html

###### last updated: May 2018

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu