**Seminars and Colloquiums**

for the week of February 5, 2018

for the week of February 5, 2018

*SPEAKERS*

*Monday*

Jerzy Dydak, University of Tennessee

Chris Manon, University of Kentucky

*Tuesday*

Xia Chen, University of Tennessee

*Wednesday*

Stefan Richter, University of Tennessee

Hamza Ruzayqat, University of Tennessee

*Thursday*

Judy Day, University of Tennessee

Zachary Bradshaw, University of Arkansas

Remus Nicoara, University of Tennessee

William H. Meeks, III, University of Massachusetts

*Friday*

William H. Meeks, III, University of Massachusetts

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday: Ayres 401
Hosted by:
*

*Delong Li & Pawel Grzegrzolka*

**Monday, February 5**

TOPOLOGY/ GEOMETRY SEMINAR

TITLE: Ends and simple coarse structures

SPEAKER: Jerzy Dydak, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 112

Abstract coarse structures were introduced by J.Roe. Subsequently, equivalent structures, called large scale structures were introduced by J.Dydak and C.Hoffland.

This talk is devoted to a much simpler definition of majority of useful coarse structures (metric, group, C_0, etc). Namely, they are equivalence relations on the set of simple ends of sets equipped with a bounded structure. As an application we show that Gromov boundary of every hyperbolic space is an example of a Higson corona and each Freundenthal compactification is an example of a Higson compactification.

ALGEBRA SEMINAR

TITLE: Problems with Khovanskii bases

SPEAKER: Chris Manon, University of Kentucky

TIME: 3:35 PM-4:25 PM

ROOM: Ayres 112

I'll give an introduction with examples to the notion of Khovanskii basis. Khovanskii bases are generating sets for algebras which are distinguished by their computational properties as well as their relationships with tropical geometry and toric geometry. After a few examples, I'll survey some recent results on their existence and classification.

**Tuesday, February 6**

STOCHASTICS/PROBABILITY SEMINAR

TITLE: Parabolic Anderson equation of a rough noise

SPEAKER: Xia Chen

TIME: 2:10 PM-3:20 PM

ROOM: Ayres 114

The model of parabolic Anderson equation with Gaussian noise has been studied extenssively in literature, especially the case when the noise is formally given as the derivative of a fractional Brownian sheet--a special but most the important case. On the otherhand, little has been known when this noise has Hurst parameter less than half, i.e., the noise contains the rough components.

This talk will be on the solvability of such equation and contains some of the most recent progress made by the speaker.

**Wednesday, February 7**

ANALYSIS SEMINAR

TITLE: ** **Pick kernels and radially weighted Besov spaces, continuation

SPEAKER: Stefan Richter, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 112

We discuss the question of which radial weights define weighted Besov spaces that are complete Pick spaces.

COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Fast Algorithms for Large Scale Unconstrained Optimization

SPEAKER: Hamza Ruzayqat

TIME: 3:35 PM-4:25 PM

ROOM: Ayres 112

Consider the following problem: Find x in R^n such that x = argmin f(y), y in R^n, where f: R^n --> R is continuously differentiable.

In many cases when n is large (10^2 - 10^6), the Hessian of f is either not available or requires a large amount of storage and computational costs. In these situations Newton's method is impractical and hard to implement. Nonlinear conjugate gradient methods, quasi-Newton methods andcombined conjugate-gradient quasi-Newton methods are more practical candidates. If a good approximation to the Hessian exists, quasi-Newton methods are much faster than conjugate gradient. In this talk, I will review several methods to solve the above optimization problem. I will focus on those that are fast and require low amount of storage

**Thursday, February 8**

MATH BIOLOGY SEMINAR

TITLE: An introduction to the methodology of model predictive control in the context of a biomedical application

SPEAKER: Judy Day, University of Tennessee

TIME: 11:10 AM-12:00 PM

ROOM: Claxton 105

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: The existence of special solutions to the Navier-Stokes equations

SPEAKER: Zachary Bradshaw, University of Arkansas

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 114

Certain special solutions to the Navier-Stokes equations are compelling candidates for irregularity formation and non-uniqueness. This talk will consist of an overview of recent advances on the existence of scaling invariant solutions to the Navier-Stokes equations as well as a discussion of a recent construction due to Tai-Peng Tsai (University of British Columbia) and Zachary Bradshaw.

JR. COLLOQUIUM

TITLE: How to teleport a goat in five easy steps

SPEAKER: Remus Nicoara, University of Tennessee

TIME: 3:40 PM-4:30 PM (Arrive at 3:20 for pizza in Ayres 408)

ROOM: Ayres 405

GEOMETRIC ANALYSIS SEMINAR

TITLE: Progress in the theory of CMC surfaces in locally homgeneous 3-manifolds

SPEAKER: William H. Meeks, III, University of Massachusetts

TIME: 5:00 PM-6:00 PM

ROOM: Ayres 113

I will go over some recent work that I have been involved in on surface geometry in complete locally homogeneous 3-manifolds X. In joint work with Mira, Perez and Ros, we have been able to finish a long term project related to the Hopf uniqueness/existence problem for CMC spheres in any such X. In joint work with Tinaglia on curvature and area estimates for CMC H>0 surfaces in such an X, we have been working on getting the best curvature and area estimates for constant mean curvature estimates in terms of their injectivity radii and their genus. It follows from this work that if W is a closed Riemannian homology 3-sphere W then the moduli space of closed embedded surfaces of constant mean curvature H in an interval [a,b] with a>0 and of genus bounded above by a positive constant is compact. In another direction, in joint work with Coskunuzer and Tinaglia we now know that in complete hyperbolic 3-manifolds N, any complete embedded surface M of finite topology is proper in N if H is at least 1 (this is work with Tinaglia) and for any value of H less than 1 there exists complete embedded nonproper planes in hyperbolic 3-space (joint work with both researchers). In joint work with Adams and Ramos, we have been able characterize the topological types of finite topology surfaces that properly embed in some complete hyperbolic 3-manifold of finite volume (including the closed case) with constant mean curvature H; in fact, the surfaces that we construct are totally umbilic

**Friday, February 9**

COLLOQUIUM

TITLE: New and old results in the classical theory of minimal and constant mean curvature surfaces in Euclidean 3-space R^3

SPEAKER: William H. Meeks, III, University of Massachusetts

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 405

In this talk I will present a survey of some of the famous problems in the classical theory of minimal and constant mean curvature surfaces in R^3. The first examples of minimal surfaces were found by Euler (catenoid) around 1741, Muesner (helicoid) around 1746 and Riemann (Riemann minimal examples) around 1860. The classical examples of non-zero constant mean curvature surfaces are the Delaunay surfaces of revolution found in 1841, which include round spheres and cylinders. My talk is full of beautiful computer graphics pictures of these and other classical surfaces which hopefully will delight the audience. My lecture will also cover the classical contributions to the calculus of variations by Plateau, Lagrange, Schwarz and Lord Kelvin.

At the end of my talk i will explain the final classification result of Meeks-Tinaglia in 2016 that the only complete simply-connected surfaces embedded in R^3 of constant mean curvature are the plane, the helicoid and round spheres (this depends on previous work of Colding-Miniz=cozzi and Meeks -Rosenberg), and the Meeks-Perez-Ros theorem that the only non-planar properly embedded minimal surfaces in R^3 of genus 0 are the classical ones found by Euler and Riemann. Finally I will mention the recent Meeks-Tinaglia theorem that the only complete annuli embedded in R^3 of constant mean curvature are Euler's catenoid and the famous revolution surfaces of Delaunay.

*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:**