# Math Calendar

### Upcoming Events

## When the outer automorphism groups of RAAGs are vast

Andrew Sale, Vanderbilt Unviersity

Location: Stevenson 1310

Right-angled Artin groups (RAAGs) are a class of groups that bridge the gap between free groups and free abelian groups. Thus, their outer automorphism groups give a way to build a bridge between GL(n,Z) and Out(Fn). We will investigate certain properties of these groups which could be described as a “vastness” property, and ask if it possible to build a boundary between those which are “vast” and those which are not. One such property is as follows: given a group G, we say G has all finite groups involved if for each finite group H there is a finite index subgroup of G which admits a map onto H. From the subgroup congruence property, it is known that the groups GL(n,Z) do not have every finite group involved for n>2. Meanwhile, the representations of Out(Fn) given by Grunewald and Lubotzky imply that these groups do have all finite groups involved. We will describe conditions on the defining graph of a RAAG that are necessary and sufficient to determine when it’s outer automorphism group has this property. The same criterion also holds for other properties, such as SQ-universality, or having a finite index subgroup with infinite dimensional second bounded cohomology. This is joint work with V. Guirardel.

## Departmental Welcome Event

Location: Stevenson 5211

Department Chair Mike Neamtu will introduce newcomers to the department. Refreshments will follow in Stevenson 1425.

## Hyperfinite realizations of abstract standard invariants

Arnaud Brothier, Vanderbilt University

Location: Stevenson 1432

To any subfactor can be associated a combinatorial object called the standard invariant. This combinatorial object can be defined abstractly. By Popa’s reconstruction theorem, any abstract standard invariant comes from a subfactor. But it is an open question to know if any standard invariant can be realized by a hyperfinite subfactor. I will discuss about hyperfinite realizations of abstract standard invariants and present new results on this matter.

## Talk Title TBA

Denis Osin, Vanderbilt University

Location: Stevenson 1310

## Talk Title TBA

Laura De Carli, Florida International University

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Akram Aldroubi)

## On the existence and uniqueness of solutions to a fluid-structure system

Igor Kukavica, University of Southern California

Location: Stevenson 1307

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. We will review the local for large and global existence results for small data. The global existence result is obtained for small initial data in a suitable Sobolev space and is based on an exponential decay of solutions. The results are joint with M. Ignatova, I. Lasiecka, and A. Tuffaha.

## Talk Title TBA

Denis Osin, Vanderbilt University

Location: Stevenson 1310

## Symplectic Calabi-Yau surfaces

Tian-Jun Li, University of Minnesota

Location: Stevenson 5211

I will survey what is known about the geometry and topology of the symplectic analogue of Calabi-Yau manifolds. The focus will be on four dimensional symplectic CYs, which resemble the Kahler CY surfaces topologically. In particular, their Betti numbers are bounded. In contrast, in higher dimension, they are known to be much more flexible via both topological and differential geometric constructions. For instance, any finitely presented group can be realized as the fundamental group of a six dimensional symplectic CY. Tea at 3:30 pm in SC 1425. (Contact Person: Ioana Suvaina)

## Talk Title TBA

Yixiang Wu, Vanderbilt University

Location: Stevenson 1307

## Workshop on Structure and Complexity in Universal Algebra, September 19 – 30, 2016

Location: TBA

## Talk Title TBA

Gili Golan, Vanderbilt University

Location: Stevenson 1310

## Talk Title TBA

Myrna Viazovska, Humbolt U of Berlin

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Ed Saff)

## Talk Title TBA

Boris Zilber, Oxford, UK

Location: Stevenson 1310

## Talk Title TBA

Lydia Bieri, University of Michigan

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Marcelo Disconzi)

## Talk Title TBA

Giusy Mazzone, Vanderbilt University

Location: Stevenson 1307

## Talk Title TBA

Richard Schwartz, Brown University

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Ed Saff)

## On convergence almost everewhere of spectral resolutions of elliptic differential operators and the multiple Fourier integrals

Ravshan Ashurov, Institute of Mathematics, National University of Uzbekistan

Location: Stevenson 1307

The question of the validity of the Luzin conjecture for the spherical partial sums of the multiple Fourier integrals is open so far. But if we consider the Riess means of the multiple Fourier integrals or in addition if we let f=0 on an open set G, and investigate the convergence to zero a.e. on G (i.e. generalized localization principle), then there are many possitive results. We first remind some of these results, and then study generalized localization principle for compactly supported distributions and present sharp conditions for its fullfilment.

## Talk Title TBA

Haynes Miller, MIT

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Anna Marie Bohmann)

## Talk Title TBA

Elaine Cozzi, Oregon State University

Location: Stevenson 1307

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