Talk_id  Date  Speaker  Title 
15384

Thursday 9/13 4:10 PM


Postdoc Lightning Talks

 Postdoc Lightning Talks
 09/13/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

15378

Thursday 9/20 4:10 PM

Brendon Rhoades, University of California, San Diego

The combinatorics, algebra, and geometry of ordered set partitions
 Brendon Rhoades, University of California, San Diego
 The combinatorics, algebra, and geometry of ordered set partitions
 09/20/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
An {\em ordered set partition} of size $n$ is a set partition of $\{1, 2, \dots, n \}$ with a specified order on its blocks. When the number of blocks equals the number of letters $n$, an ordered set partition is just a permutation in the symmetric group $S_n$. We will discuss some combinatorial, algebraic, and geometric aspects of permutations (due to MacMahon, Carlitz, Chevalley, Steinberg, Artin, LusztigStanley, Ehresmann, Borel, and LascouxSch\"utzenberger). We will then describe how these results generalize to ordered set partitions and discuss a connection with the HaglundRemmelWilson {\em Delta Conjecture} in the field of Macdonald polynomials. Joint with Jim Haglund, Brendan Pawlowski, and Mark Shimozono.

15381

Thursday 9/27 4:10 PM

Igor Dolgachev, University of Michigan

The reflection group of a regular tetrahedron
 Igor Dolgachev, University of Michigan
 The reflection group of a regular tetrahedron
 09/27/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
I will explain how the group of affine orthogonal transformations generated by the reflections into the four facets of a regular tetrahedron and its symmetries appears as a discrete group of motions of the 9dimensional hyperbolic space, as the full group of automorphisms of some algebraic surfaces and as a lattice in a projective linear group over the 3adic numbers.

15420

Thursday 10/4 4:10 PM

Yang Yang, Michigan State University

Some inverse source and coefficient problems for the wave operators (special colloquium)
 Yang Yang, Michigan State University
 Some inverse source and coefficient problems for the wave operators (special colloquium)
 10/04/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
Inverse problems seek to infer causal factor from the resulting observation, and waves are among the most prevalent and significant observations in nature. In this talk, we will discuss two inverse problems for the acoustic wave equation and its generalizations. The first is an inverse source problem where one attempts to determine an instantaneous source from the boundary Dirichlet data. We give sharp conditions on unique and stable determination, and derive an explicit reconstruction formula for the source. The second is an inverse coefficient problem on a cylinderlike Lorentzian manifold (M,g) for the Lorentzian wave operator perturbed by a vector field A and a function q. We show that local knowledge of the DirichlettoNeumann map (DNmap) stably determines the jets of (g,A,q) up to gauge transformations, and global knowledge of the DNmap stably determines the lens relation of g as well as the light ray transforms of A and q. This is based on joint work with P. Stefanov.

14349

Thursday 10/11 4:10 PM

Deanna Needell, University of California, Los Angeles

Simple Classification from Binary Data
 Deanna Needell, University of California, Los Angeles
 Simple Classification from Binary Data
 10/11/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
Binary, or onebit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this talk, we provide a brief background to sparsity and 1bit measurements, and then present new results on the problem of data classification from binary data that proposes a framework with low computation and resource costs. We illustrate the utility of the proposed approach through stylized and realistic numerical experiments, provide a theoretical analysis for a simple case, and discuss future directions.

14361

Thursday 10/18 4:10 PM

Frank Morgan, Williams College

Double Soap Bubbles and Densities
 Frank Morgan, Williams College
 Double Soap Bubbles and Densities
 10/18/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
The familiar double soap bubble is the leastarea way to enclose and separate two given volumes in Euclidean space. What if you give space a density, such as r^2 or e^r^2 or e^r^2? The talk will include recent results and open questions. Students welcome.

16453

Thursday 11/1 10:00 AM

Andrew Krause, MSU

TBA (special colloquium)
 Andrew Krause, MSU
 TBA (special colloquium)
 11/01/2018
 10:00 AM  11:00 AM
 C304 Wells Hall
TBA

15382

Thursday 11/1 4:10 PM

Rustum Choksi, McGill University

Nonlocal Geometric Variational Problems: Isotropic and Anisotropic Extensions of Gamow's Liquid Drop Problem and Beyond
 Rustum Choksi, McGill University
 Nonlocal Geometric Variational Problems: Isotropic and Anisotropic Extensions of Gamow's Liquid Drop Problem and Beyond
 11/01/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
The liquid drop (LD) model, an old problem of Gamow for the shape of atomic nuclei, has recently resurfaced within the framework of the modern calculus of variations. The problem takes the form of a nonlocal isoperimetric problem on all 3space with nonlocal interactions of Coulombic type.
In this talk, we first state and motivate the LD problem, and then summarize the state of the art for global minimizers.
We then address certain recent anisotropic variants of the LD problem in the small mass regime, with a particular focus on the minimality of the Wulff shape.
In the second half of the talk, we address a related nonlocal geometric problem based solely on competing interaction potentials of algebraic type. This problem is directly related to a wide class of selfassembly/aggregation models for interacting particle systems (eg. swarming).
This talk includes joint work with Almut Burchard (Toronto), Robin Neumayer (IAS and Northwestern), and Ihsan Topaloglu (Virginia Commonwealth).

16456

Monday 11/5 10:00 AM

Telma Gracias

TBA (special colloquium)
 Telma Gracias
 TBA (special colloquium)
 11/05/2018
 10:00 AM  11:00 AM
 C304 Wells Hall
No abstract available.

14362

Thursday 11/8 4:10 PM

Jared Speck

Singularity Formation in General Relativity
 Jared Speck
 Singularity Formation in General Relativity
 11/08/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
The celebrated Hawking–Penrose theorems are breakdown results for solutions to the Einstein equations of general relativity, which are a system of highly nonlinear wavelike PDEs. These theorems show that, under appropriate assumptions on the matter model, a large, open set of initial data lead to geodesically incomplete solutions. However, these theorems are “soft” in that they do not yield any information about the nature of the incompleteness, leaving open the possibilities that i) it is tied to the blowup of some invariant quantity (such as curvature) or ii) it is due to a more sinister phenomenon, such as incompleteness stemming from lack of information for how to uniquely continue the solution (this is roughly known as the formation of a Cauchy horizon). In various works, some joint with I. Rodnianski, we have obtained the first results in more than one spatial dimension that eliminate the ambiguity for an open set of initial data: for the solutions that we studied, the incompleteness is tied to the blowup of various spacetime curvature scalars along a spacelike hypersurface. Physically, this phenomenon corresponds to the stability of the Big Bang and/or Big Crunch singularities. From an analytic perspective, the main theorems are stable blowup results for quasilinear systems of elliptichyperbolic PDEs. In this talk, I will provide an overview of these results and explain how they are tied to some of the main themes of investigation by the mathematical general relativity community. I will also discuss the role of geometric and gauge considerations in the proofs, as well as intriguing connections to other problems concerning stable singularity formation.

16454

Friday 11/9 10:00 AM

Tsz Ho Chan, University of Memphis

TBA (special colloquium)
 Tsz Ho Chan, University of Memphis
 TBA (special colloquium)
 11/09/2018
 10:00 AM  11:00 AM
 C304 Wells Hall
TBA

16469

Thursday 12/13 4:10 PM

Noam Elkies, Harvard University

Sphere Packing from Cerium to Viazovska
 Noam Elkies, Harvard University
 Sphere Packing from Cerium to Viazovska
 12/13/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
The sphere packing problem in dimension $n$ asks:
How densely can one pack identical Euclidean balls in $\mathbb{R}^n$ with
disjoint interiors? We review some of this problem's history and
connections with various areas of mathematics and science.
Some special values of $n$, notably $8$ and $24$, allow for remarkably
tight and symmetrical configurations that have long been suspected
to be the densest possible in those dimensions. We conclude with the
series of recent results culminating with Viazovska's breakthrough that
led to the solution of the sphere packing problem for $n=8$ and $n=24$.
