**Seminars and Colloquiums**

for the week of November 6, 2017

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:**