Seminars & Events for 2015-2016

October 9, 2015
1:45pm - 2:45pm
Real Gromov-Witten theory in all genera

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces.

Speaker: Penka Georgieva, Jussieu
Location:
Fine Hall 322
October 9, 2015
3:00pm - 4:00pm
Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic maps - Part 1

This series of talks is an extension of the colloquium talk where we outline a proof of recent results concerning the structure of stationary and minimizing harmonic maps.  Specifically, we will show that the singular stratum S^k(f) are k-rectifiable for a stationary map, and for a minimizing map that the singular set S(f) has finite n-3 measure.  We will also show sharp sobolev estimates for s

Speaker: Aaron Naber , Northwestern University
Location:
Fine Hall 314
October 9, 2015
4:00pm - 5:00pm
Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic maps (Part 2)

This series of talks is an extension of the colloquium talk where we outline a proof of recent results concerning the structure of stationary and minimizing harmonic maps.  Specifically, we will show that the singular stratum S^k(f) are k-rectifiable for a stationary map, and for a minimizing map that the singular set S(f) has finite n-3 measure.  We will also show sharp sobolev estimates for s

Speaker: Aaron Naber , Northwestern University
Location:
Fine Hall 314
October 12, 2015
3:00pm - 4:00pm
$\ell^p(\mathbf Z^d)$ boundedness for discrete operators of Radon types: maximal and variational estimates

PLEASE NOTE ROOM CHANGE FROM LAST TERM:  SEMINAR WILL NOW BE HELD IN FINE 110.    In recent times - particularly the last two decades - discrete analogues in harmonic analysis have gone through a period of considerable changes and developments. This is due in part to Bourgain's pointwise ergodic theorem for the squares on $L^p(X, \mu)$ for any $p>1$.

Speaker: Mariusz Mirek, Bonn University
Location:
Fine Hall 110
October 12, 2015
4:30pm - 5:30pm
Comparison Lemmas and Convex-Optimization-Based Signal Recovery

In the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, finite constellation, etc.) from (possibly) noisy measurements in a variety of applications in statistics, signal processing, machine learning, communications, etc.

Speaker: Babak Hassibi , Caltech
Location:
Fine Hall 214
October 13, 2015
4:30pm - 6:00pm
Local volumes and equisingularity theory

The epsilon multiplicity of a module is a natural generalization of the Hilbert-Samuel multiplicity of an ideal. It can be expressed as the volume of a suitable Cartier divisor associated with the module. In this talk, I will present a result that determines the change of the epsilon multiplicity of a module across flat families.

Speaker: Antoni Rangachev, Northeastern University
Location:
Fine Hall 322
October 14, 2015
3:00pm - 4:00pm
Harmonicity and Invariance on the Slice

The subject of this talk is the slice of the discrete cube - i.e. the uniform distribution over all binary vector of a certain weight, or probabilistically the product measure on the cube conditioned on having a specific sum.

Speaker: Elchanan Mossel, University of Pennsylvania
Location:
Fine Hall 214
October 15, 2015
12:30pm - 1:30pm
Embeddings into Euclidean space and related obstructions

We will discuss several results about bi-Lipschitz embeddings of metric spaces into Hilbert space, motivated by related classic theorems in Banach spaces. Emphasis will be given on techniques for proving non-embeddability and Ramsey-type theorems in this context.

Speaker: Alex Eskenazis, Princeton University
Location:
Fine Hall 314
October 15, 2015
2:00pm - 3:30pm
Polygonal Outer Billiards

I will introduce the polygonal outer billiards problem, presenting a bit of history, open problems, and connections to other dynamical systems. I will focus on the case of regular polygons.

Speaker: In-Jee Jeong, Princeton University
Location:
Fine Hall 601
October 15, 2015
4:30pm - 5:30pm
The Taylor model in magnetohydrodynamics

Please note double seminar on this date.   We shall discuss a model introduced by J.B. Taylor in 1963, that comes from a formal asymptotic limit of MHD (magnetohydrodynamics) equations with rotation. This asymptotic model, relevant to the Earth's dynamo problem, should in principle allow for easier numerics.

Speaker: David Gerard-Varet , Paris 7
Location:
Fine Hall 322
October 15, 2015
4:30pm - 5:30pm
Casson towers and slice knots

A link is slice if it is the boundary of a disjoint union of flat discs in the 4-ball. The link slicing problem is closely related to the surgery and s-cobordism programme for classifying 4-manifolds. A Casson tower is a 4-manifold with boundary built from iteratively attempting to find an embedded disc in a 4-manifold using immersed discs.

Speaker: Mark Powell, Université de Québec à Montreal (UQAM)
Location:
Fine Hall 314
October 15, 2015
4:30pm - 5:30pm
Adjoint Selmer groups for polarized automorphic Galois representations

Given the p-adic Galois representation associated to a regular algebraic polarized cuspidal automorphic representation, one naturally obtains a pure weight zero representation called its adjoint representation. Because it has weight zero, a conjecture of Bloch and Kato says that the only de Rham extension of the trivial representation by this adjoint representation is the split extension.

Speaker: Patrick Allen , UIUC
Location:
IAS Room S-101
October 15, 2015
4:30pm - 6:00pm
Clique-stable set separation

Consider the following communication complexity problem: Alice is given a clique K, Bob is given a stable set S, and they have to decide via a non-deterministic protocol whether K intersects S or not. A ``certificate'' for the non-intersection is a bipartition of the vertices such that K is included in one side, and S is included in the other side.

Speaker: Aurelie Lagoutte, University of Lyon
Location:
Fine Hall 224
October 15, 2015
5:30pm - 6:30pm
The Hele-Shaw and Muskat problem

Please note double seminar on this date.  In this talk we are going to review some recent results concerning the evolution of a free boundary under Darcy's flow. This is known as the Muskat problem or the Hele-Shaw cell problem with gravity. In particular, we will present a new method based on the study of the bulk rather than the appropriate integral equation.

Speaker: Rafael Granero-Belinchón, UC Davis
Location:
Fine Hall 322
October 16, 2015
3:00pm - 4:00pm
Embedded Willmore tori in three-manifolds with small area constraint

While there are lots of contributions on Willmore surfaces in the three-dimensional Euclidean space, the literature on curved manifolds is still relatively limited. One of the main aspects of the Willmore problem is the loss of compactness under conformal transformations.

Speaker: Andrea Malchiodi, Scuola Normale Superiore-Pisa
Location:
Fine Hall 314
October 16, 2015
3:00pm - 4:00pm
3d mirror symmetry and symplectic duality

Please note special location (Fine 224) and time (3:00-4:00).   In recent work of Braden, Licata, Proudfoot, and Webster, a "symplectic duality" was described between pairs of module categories O(M), O(M') associated to certain pairs of complex symplectic manifolds (M, M').

Speaker: Tudor Dimofte , Perimeter Institute
Location:
Fine Hall 224
October 16, 2015
4:15pm - 5:15pm
The two membranes problem

We will consider the two membranes obstacle problem for two different operators, possibly non-local. In the case when the two operators have different orders, we discuss how to obtain $C^{1,\gamma}$ regularity of the

Speaker: Daniela Da Silva, Columbia University
Location:
Fine Hall 314
October 19, 2015
3:15pm - 4:30pm
A restriction estimate using polynomial partitioning

The restriction conjecture is an open problem in Fourier analysis first raised by Stein in the late 60’s. It is about the L^p estimates obeyed by an oscillatory integral operator. I will explain a recent approach to this problem, which gives a slightly better estimate in three dimensions.

Speaker: Larry Guth , MIT
Location:
Fine Hall 110
October 19, 2015
4:30pm - 5:30pm
Applications of interlacing polynomials in graph theory

In this talk, I will discuss some recent applications of interlacing polynomials in graph theory. I will begin by discussing the more classical results concerning graph polynomials, including the real rootedness of the matching polynomial and the extension of Chudnovsky and Seymour to the independence polynomial of claw-free graphs. I will then discuss results using the ``method of interlacing

Speaker: Adam Marcus , Princeton University
Location:
Fine Hall 214
October 20, 2015
4:30pm - 6:00pm
On Minkowski bases for Newton-Okounkov bodies

The Newton-Okounkov bodies of linear series on an n-dimensional projective variety is a compact convex body in real n-space which carries information about the linear series. However, in general it is hard to determine in practice. We show that under certain conditions there exist simple "building blocks" for al Newton-Okounkov bodies of a given variety, a so called Minkowski basis.

Speaker: David Schmitz , Stony Brook University
Location:
Fine Hall 322

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