**Seminars and Colloquiums**

for the week of March 4, 2019

for the week of March 4, 2019

*SPEAKERS*

**Monday
** Ryan Unger, University of Tennessee

**Wednesday**

Cheng Chu, Vanderbilt University

Steve Wise, University of Tennessee

**Thursday**

Andre Neves, University of Chicago

**Friday**

Andre Neves, University of Chicago

**TEA TIME** - Canceled

3:00 PM – 3:30 PM

Monday, Tuesday & Wednesday

Room: Ayres 401

Hosted by:

Topics:

**Monday, 3/4**

**GEOMETRIC ANALYSIS READING SEMINAR
**TITLE: Fine time extinction of Ricci flow with bubbling off II

SPEAKER: Ryan Unger, University of Tennessee

TIME: 3:35 PM-5:30 PM

ROOM: Ayres 113

I will continue with the proof of finite time extinction for irreducible manifolds with nonzero pi_3.

**Wednesday, 3/6**

**ANALYSIS SEMINAR**

TITLE: Reducing Subspaces of de Branges-Rovnyak Spaces

SPEAKER: Cheng Chu, Vanderbilt University

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 113

The de Branges-Rovnyak space H(b) is a Hilbert space contractively contained in the Hardy space of the unit disk that is invariant under the backward shift operator. We study reducing subspaces of the square of backward shift operator on H(b).

Douglas and Foias considered the problem when b is an inner function. We use another approach to extend their result to the case where b is an extreme function.

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

TITLE: Convergence Analyses of some Nonlinear Multi-Level Algorithms for Non-Quadratic Convex Optimization Problems via Space Decomposition and Subspace Correction, Part IV of IV

SPEAKER: Steve Wise, University of Tennessee

TIME: 3:35 PM-4:25 PM

ROOM: Ayres 113

Nonlinear multi-level methods, such as the full approximation storage (FAS) multigrid scheme, are widely used solvers for nonlinear problems. In this paper, a new framework to analyze FAS-type methods for convex optimization problems is developed. FAS can be recast as an inexact version of a nonlinear multigrid method based on space decomposition and subspace correction, namely the successive subspace optimization (SSO) method of Jinchao XU and coauthors. The theory is quite general and is an abstraction of both SSO and the preconditioned steepest descent (PSD) method. In our algorithm, we show that the local problem in each subspace can be simplified to be linear and one gradient decent iteration is enough to ensure linear convergence of the FAS scheme. In Part I, I will introduce the terminology and primary assumptions, and we will give an improved convergence result for SSO in a Hilbert space setting. Then we will motivate and define the generalized FAS algorithm.

This work is joint with Long Chen and Xiaozhe Hu

**Thursday, 3/7**

**GEOMETRIC ANALYSIS SEMINAR
**TITLE: Density and equidistribution of minimal surfaces

SPEAKER: Andre Neves, University of Chicago

TIME: 5:45 PM-7:00 PM (note change)

ROOM: Ayres 113

We will show that on closed manifolds, the set of all closed minimal surfaces is dense for generic metrics. Moreover, under the same conditions, we will also show the existence of a sequence of minimal surfaces that become equidistributed. These are the first results of this kind for minimal hypersurfaces. This is joint work with Irie, Marques, and Song.

**Friday, 3/8**

**COLLOQUIUM
**TITLE: Recent progress on existence of minimal surfaces

SPEAKER: Andre Neves, University of Chicago

TIME: 2:35 PM-3:35 PM (note change)

ROOM: Ayres 405

Please note that this week’s colloquium will be held one hour early at 2:35 PM.

A long standing open question in geometry was proposes by Yau 30 years ago and asks whether every closed manifold has an infinite number of closed minimal surfaces. Over the last year dramatic progress occurred and, thanks to the work of several people, we now know that Yau’s conjecture holds, minimal surfaces become equidistributed (generically), and their area obeys a universal Weyl Law. I will survey these developments.

*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 mlangfo5@utk.edu *

**Past notices:**

Winter Break