# Seminars & Events for 2014-2015

##### Propagation enhancement of reaction-diffusion fronts by a line of fast diffusion

We discuss here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. By 'strong diffusion', we mean a large multiple of the Laplacian, or the fractional laplacian. The question is the asymptotic (as time goes to infinity) speed of spreading in the direction of the line and in the plane.

##### Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets

One of the major themes of the analytic theory of automorphic forms is the connection between equidistribution and subconvexity. An early example of this is the famous result of Duke showing the equidistribution of Heegner points on the modular surface, a problem that boils down to the subconvexity problem for the quadratic twists of Hecke-Maass L-functions.

##### Taut foliations, left-orderability, and cyclic branched covers

##### Cyclic homology and S^1-equivariant symplectic cohomology

In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is S^1-equivariant, at a suitable chain level.

##### Quantitative uniqueness, doubling lemma and nodal sets

Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property.

##### TBA - Hintz

##### Eigenvector Centralities for Temporal Networks

Motivated by a series of examples (the U.S. Ph.D. exchange in mathematics, co-starring relationships among top-billed actors in Hollywood, and co-citations between U.S. Supreme Court decisions), we study the general problem of calculating eigenvector centralities as generalized to temporal directed network data.

##### Interface dynamics for incompressible flows

The goal of these lectures is to present the main ideas and arguments of recent results concerning global solutions and finite time singularities for interface dynamics. In particular those contour dynamics that are given by basic fluid mechanics systems; Euler´s equation, Darcy´s law and the Quasi-geostrophic equation.

##### When Exactly Do Quantum Computers Provide a Speedup?

Twenty years after the discovery of Shor's factoring algorithm, I'll survey what we now understand about the structure of problems that admit quantum speedups. I'll start with the basics, discussing the hidden subgroup, amplitude amplification, adiabatic, and linear systems paradigms for quantum algorithms. Then I'll move on to some general results, obtained by Andris Ambainis and myself over

##### TBA - Nori

##### Interface dynamics for incompressible flows

The goal of these lectures is to present the main ideas and arguments of recent results concerning global solutions and finite time singularities for interface dynamics. In particular those contour dynamics that are given by basic fluid mechanics systems; Euler´s equation, Darcy´s law and the Quasi-geostrophic equation.

##### TBA - McLean

**Please note special day.**

##### Central Limit Theorems and Lee-Yang Zeros

I will describe some old and some new results (joint work with Pittel, Ruelle, Speer) on how to derive Central Limit Theorems and even Local Central Limit Theorems from information about the location of zeros of the generating function. Applications to the distribution of eigenvalues of random matrices, graph counting polynomials, and statistical mechanical systems will be given.

##### Automorphic L-functions and descent method

Automorphic L-functions are fundamental invariants attached to a given cuspidal automorphic representation of a reductive group G. In addition to arithmetic applications, automorphic L-functions are used to characterize various types of Langlands functorial transfers.

##### Rationality of Algebraic Varieties

Finding a rational parametrization for a system of polynomial equations has been studied for a long time, and it leads to the concept of rational varieties. Bézout’s theorem implies that degree 1 and 2 hypersurfaces are rational. It is a hard problem to determine whether a general variety is rational.

##### Unbounded orbits for the cubic nonlinear Schrodinger equation in the semi periodic setting

A natural question in the study of nonlinear dispersive equations is to describe their asymptotic behavior. In the Euclidean plane, in great generality, global solutions scatter (i.e. asymptotically follow a linear flow).

##### The Persistent Homology Group

The persistence of a function f: X -> R is a collection of measurements, one for each open interval of the real line. We call each measurement a persistent homology group. If f is stratifiable, then its persistence can be visualized by something called the persistence diagram. The persistent homology group is special because it is stable to perturbations of the function f. Through the le

##### On the number of rich lines in truly high dimensional sets

We prove a new upper bound on the number of r-rich lines (lines with at least r points) in a `truly' d-dimensional configuration of points v_1,...,v_n over the complex numbers. More formally, we show that, if the number of r-rich lines is significantly larger than n^2/r^d then there must exist a large subset of the points contained in a hyperplane.

##### Heegaard Floer homologies and cuspidal curves

##### Level raising mod 2 and arbitrary 2-Selmer ranks

We prove a level raising mod p=2 theorem for elliptic curves over Q, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by explaining our motivation from W. Zhang's approach to the p-part of the BSD conjecture.