# Upcoming Seminars & Events

## Primary tabs

October 6, 2015
4:30pm - 5:30pm
##### The reasonable effectiveness of mathematical deformation theory in physics, especially quantum mechanics and maybe elementary particle symmetries
###### Mathematical Physics Seminar

In 1960 Wigner marveled about the unreasonable effectiveness of mathematics in the natural sciences," referring mainly to physics. In that spirit we shall first explain how a posteriori relativity and quantum mechanics can be obtained from previously known theories using the mathematical theory of deformations. After a tachyonic overview of how the standard model of elementary particles arose from empirically guessed symmetries we indicate how these symmetries could (very reasonably) be obtained from those of relativity using deformations (including quantization). This poses difficult and interesting mathematical problems with potentially challenging applications to physics.

Speaker: Daniel Sternheimer , Rikkyo University & Université de Bourgogne
Location:
October 6, 2015
4:30pm - 6:00pm
##### The geometric constants in Manin's Conjecture
###### Algebraic Geometry Seminar

Manin's Conjecture predicts that the growth of points of bounded height is controlled by certain geometric constants. I will analyze the geometry underlying these constants and discuss applications to Manin's Conjecture. A key tool is the minimal model program.

Speaker: Brian Lehmann, Boston College
Location:
Fine Hall 322
October 7, 2015
4:30pm - 6:00pm
##### Singular Sets of Geometric PDE's
###### Department Colloquium

Given a solution of a nonlinear pde the two primary issues regarding the regularity theory are a priori estimates and the structure of the singular set. We will discuss new techniques in the analysis of these issues, which have been particularly successful in the study of geometrically motivated equations. To pick an example: in the context of a stationary harmonic map f:M->N between Riemannian manifolds we will see that the singular set S(f) may be stratified into pieces S^k(M) which are k-rectifiable. If f is minimizing harmonic map then we will see that the singular set S(f) has finite n-3 measure, and has apriori estimates in weak L^3 , both of which are sharp estimates. The techniques of the proofs are quite general and include the quantitative stratification, W^{1,p}-Reifenberg results, and L^2 -subspace approximation results, and also work to give sharp estimates for minimal surfaces and other geometric equations. We will try and give an understandable introduction to these topics. This is joint work with Daniele Valtorta.

Speaker: Aaron Naber, Northwestern University
Location:
Fine Hall 314
October 8, 2015
2:00pm - 3:30pm
##### On Rauzy Induction: Bufetov's Questions
###### Ergodic Theory & Statistical Mechanics

Given an interval exchange transformation (IET) and a sub-interval, there arises a natural visitation matrix that relates the induced IET to the original IET. We show that the original IET, up to topological conjugacy, may be recovered from successive visitation matrices. This answers a question by A. Bufetov and generalizes work by W. A. Veech, which considered the case when the matrices arise from Rauzy induction. Furthermore, we provide an effective proof of Veech's result. That is to say, we will show how to find the necessary data for an IET given only a finite number of such visitation matrices.

Speaker: Jon Fickenscher, Princeton University
Location:
Fine Hall 601
October 8, 2015
3:00pm - 4:00pm
##### Augmented trees with high girth
###### Discrete Mathematics Seminar

Let G be a graph consisting of a complete binary tree of depth h together with a back edge from each leaf connecting it to one of its ancestors. Suppose further that the girth of G exceeds g. What is the minimum possible depth h=h(g) in such a graph ? This question is motivated by results in a joint paper with Kostochka, Reiniger, West and Zhu, where these graphs are used to provide simple explicit constructions of graphs and hypergraphs of high girth and high chromatic number, as well as tight examples of sparse high girth bipartite graphs with large list-chromatic number.

Speaker: Noga Alon , Tel Aviv University
Location:
Fine Hall 224
October 8, 2015
4:30pm - 5:30pm
##### Algebraic solutions of differential equations over the projective line minus three points
###### Princeton University/IAS Number Theory Seminar

The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on the projective line minus three points. In this talk, I will first focus on this case and introduce a p-adic convergence condition, which would hold if the p-curvature is defined and vanishes. Using the algebraicity criteria established by André, Bost, and Chambert-Loir, I will prove a variant of this conjecture for the projective line minus three points, which asserts that if the equation satisfies the above convergence condition for all p, then its monodromy is trivial. I will also prove a similar variant of the p-curvature conjecture for an elliptic curve with j-invariant 1728 minus its identity point.

Speaker: Yunqing Tang, Harvard University
Location:
Fine Hall 214
October 8, 2015
4:30pm - 5:30pm
##### A probabilistic approach to the Navier-Stokes equations
###### Analysis of Fluids and Related Topics

In this preliminary talk, we consider the regularity issues of the incompressible Navier-Stokes equations on the basis of probabilistic methods. In the stream function (vector potential) formulation, the Navier-Stokes equations are recast in path-integral forms by "the Feynman-Kac formula". We discuss the regularity of solutions on this basis.

Speaker: Koji Ohkitani, University of Sheffield
Location:
Fine Hall 322
October 9, 2015
2:00pm - 3:00pm
##### Real Gromov-Witten theory in all genera
###### Symplectic Geometry Seminar

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. This allows us to endow the uncompactified moduli spaces of real maps from symmetric surfaces of all topological types with natural orientations and to verify that they extend across the codimension-one boundaries of these spaces. In reasonably regular cases, these invariants can be used to obtain lower bounds for counts of real curves of arbitrary genus. Joint work with A. Zinger.

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
###### Differential Geometry & Geometric Analysis Seminar

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 solutions.  The first lecture will focus on a new series of Reifenberg-type results.  Specifically, we give criteria under which a set in R^n can be shown to be rectifiable with uniform k-dim hausdorff measure estimates.  Such a result is only useful of course if we can apply it to a concrete situation, and in order to apply this to the singular stratum S^k(f) we prove a new L^2 subspace approximation theorem.  In the second lecture we will discuss this in detail, as well as the quantitative stratification, which allows us to decompose S^k into more controllable pieces for the analysis.  This is joint work with Daniele Valtorta.

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
###### Analysis Seminar

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 $p>1$. The main aim of this talk is to discuss recent developments in discrete harmonic analysis. We will be mainly concerned with $\ell^p(\mathbf Z^d)$ estimates $(p>1)$ of $r$-variations $(r>2)$ for discrete averaging operators and singular integral operators along polynomial mappings. All the results are subjects of the ongoing projects with Elias M. Stein and Bartosz Trojan.

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

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. I will describe a fairly general theory for how to determine the performance (minimum number of measurements, mean-square-error, probability-of-error, etc.) of such methods for certain measurement ensembles (Gaussian, Haar, quantized Gaussian, etc.). Among other results, we shall show that the expression for the mean-square error of the LASSO algorithm is identical to that of classical least squares, provided the ambient dimension of the unknown signal is replaced by its “statistical dimension”, and that the performance of the box relaxation for recovering BPSK signals in communications comes within 3 db of the celebrated “matched filter bound”. The genesis of the theory can be traced back to an inconspicuous 1962 lemma of Slepian (on comparing Gaussian processes).

Speaker: Babak Hassibi , Caltech
Location:
Fine Hall 214
October 13, 2015
4:30pm - 6:00pm
##### Local volumes and equisingularity theory
###### Algebraic Geometry Seminar
Speaker: Antoni Rangachev, Northeastern University
Location:
Fine Hall 322
October 14, 2015
3:00pm - 4:00pm
##### Harmonicity and Invariance on the Slice
###### Probability Seminar

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. I will review the L_2 theory of the slice as well as a the following new result: functions of low degree have similar distribution on the slice and the corresponding product measure on the cube. The proof relates harmonicity to decomposition of increasing path in terms of a Markov chain and a reverse Markov chain. Based on a joint work with Yuval Filmus (http://arxiv.org/abs/1507.02713).

Speaker: Elchanan Mossel, University of Pennsylvania
Location:
Fine Hall 214
October 15, 2015
2:00pm - 3:30pm
##### TBA - Maria Avdeeva
###### Ergodic Theory & Statistical Mechanics
Speaker: Maria Avdeeva, Princeton University
Location:
Fine Hall 601
October 15, 2015
4:30pm - 5:30pm
##### TBA- Patrick Allen
###### Princeton University/IAS Number Theory Seminar
Speaker: Patrick Allen , Northwestern University
Location:
IAS Room S-101
October 15, 2015
4:30pm - 5:30pm
##### TBA - Mark Powell
###### Topology Seminar
Speaker: Mark Powell, Université de Québec à Montreal (UQAM)
Location:
Fine Hall 314
October 15, 2015
4:30pm - 6:00pm
##### TBA - Aurelie Lagoutte
###### Discrete Mathematics Seminar
Speaker: Aurelie Lagoutte, University of Lyon
Location:
Fine Hall 224
October 15, 2015
4:30pm - 5:30pm
##### TBA - David Gerard-Varet
###### Analysis of Fluids and Related Topics
Speaker: David Gerard-Varet , Paris 7
Location:
Fine Hall 322
October 15, 2015
5:30pm - 6:30pm
##### TBA - Rafael Granero
###### Analysis of Fluids and Related Topics

Please note double seminar on this date.

Speaker: Rafael Granero, UC Davis
Location:
Fine Hall 322
October 16, 2015
2:00pm - 3:00pm
##### TBA - Tudor Dimofte
###### Symplectic Geometry Seminar
Speaker: Tudor Dimofte , Perimeter Institute
Location:
Fine Hall 322