# Math Calendar

### Upcoming Events

## The Twisted Nature of Polyominoes

Alex Vlasiuk, Vanderbilt University

Location: Stevenson 1206

Polyominoes are flat geometric figures obtained by joining several equal squares edge to edge. They can tile the plane, help you play Tetris or Blokus, serve as a literary subject or a test case for your programming/counting skills, or simply be the building blocks of many a joyous pastime. But for all that flatness, there’s a certain twist to them. (Pizza and drinks will be provided.)

## Seiberg-Witten Theory and Geometry of 4-Manifolds

Ioana Suvaina, Vanderbilt University

Location: Stevenson 1310

The Seiberg-Witten theory provides a smooth invariant, which can be used to distinguish homeomorphic, non-diffeomorphic, smooth structures. It also has a deep impact on the Riemannian properties of 4-manifolds. We will discuss how obstructions to the existence of Einstein metrics arise, and how one can compute the Yamabe invariant for Kahler surfaces and some symplectic 4-manifolds.

## A Bieberbach Theorem for Crystallographic Group Extensions

John Ratcliffe, Vanderbilt University

Location: Stevenson 1310

Joint work with Steven Tschantz. We will talk about our relative Bieberbach theorem: For each dimension n there are only finitely many isomorphism classes of pairs of groups (Γ,N) such that Γ is an n-dimensional crystallographic group and N is a normal subgroup of Γ such that Γ/N is a crystallographic group. This result is equivalent to the statement that for each dimension n there are only finitely many affine equivalence classes of geometric orbifold fibrations of compact, connected, flat n-orbifolds.

## The Einstein Equations and Gravitational Wave

Lydia Bieri, University of Michigan

Location: Stevenson 5211

In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. This system of hyperbolic nonlinear pde has served as a playground for all kinds of new problems and methods in pde analysis and geometry. A major goal in the study of these equations is to investigate the analytic properties and geometries of the solution spacetimes. In particular, fluctuations of the curvature of the spacetime, known as gravitational waves, have been a highly active research topic. Last year, gravitational waves were observed for the first time by LIGO. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will talk about geometric-analytic results on gravitational radiation and the memory effect of gravitational waves. We will connect the mathematical findings to experiments. I will also address recent work with David Garfinkle on gravitational radiation in asymptotically flat as well as cosmological spacetimes.Tea at 3:30 pm in SC 1425. (Contact Person: Marcelo Disconzi)

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Giusy Mazzone, Vanderbilt University

Location: Stevenson 1307

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Sandeepan Parekh, Vanderbilt University

Location: Stevenson 1432

## Department Picnic

Location: Edwin Warner Park, Shelter 11

Departmental Fall Picnic. For more information contact Graduate Students Sahana Balasubramanya or Bryan Jacobson.

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John Jasper, University of Cincinatti

Location: Stevenson 1432

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Brent Nelson, UC Berkeley

Location: Stevenson 1432

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Ben Hayes, Vanderbilt University

Location: Stevenson 1310

## Sharp Energy Minimization for the Triangular Bi-Pyramid

Richard Schwartz, Brown University

Location: Stevenson 5211

For any s>0 one can define the Riesz s-energy potential for a finite configuration of points on the sphere as the sum of the reciprocal s powers of the distances between the points, taken over all pairs. The case of 5 points has been notoriously intractable and it has been long conjectured that there exists a constant S = 15.048… such that the triangular bi-pyramid is the global minimizer for the Riesz s-energy potential if and only if s in (0,S]. I will explain my very recent proof of this result. The argument has some massive (but rigorous) computer calculations in it, but it also involves such ideas as stereographic projection, symmetrization, polynomial interpolation, and divide-and-conquer algorithms. I’ll illustrate the talk with a bunch of computer demos. Tea at 3:30 pm in SC 1425. (Contact Person: Ed Saff)

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Craig Kleski, Miami University in Ohio

Location: Stevenson 1432

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Hung-Chang Liao, Penn State University

Location: Stevenson 1432

## On Convergence Almost Everywhere 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.

## The Trouble with Voting

Zach Gaslowitz, Vanderbilt University

Location: Stevenson 1206

We will explore some of the surprising mathematical challenges one runs into when trying to turn a pile of ballots into a single winner. How do we decide who should win, and how does this question influence our democracy as a whole?

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Haynes Miller, MIT

Location: Stevenson 5211

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

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Elaine Cozzi, Oregon State University

Location: Stevenson 1307

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Daniel Drimbe, UC San Diego

Location: Stevenson 1432

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Nigel Higson, Penn State

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Rudy Rodsphon)

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Danny Calegari, University of Chicago

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Mark Sapir)

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