# Seminars & Events for 2016-2017

##### A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold

We prove a sharp inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. This inequality generalizes the classical Minkowski inequality for surfaces in the three dimensional Euclidean space, and has a natural interpretation in terms of the Penrose inequality for collapsing null shells of dust.

##### Subexponential growth, measure rigidity, strong property (T) and Zimmer's conjecture

Lattices in higher rank simple Lie groups, like SL(n,R) for n>2, are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actio

##### Possible lattice distortions in the Hubbard model for graphene

**Please note special time and location.**

##### Lagrangian analyticity in fluid mechanics

The incompressible Euler equations imply that the Lagrangian trajectories of individual water particles are automatically analytic in time, as long as the velocity field is slightly better than differentiable in the space variables. We'll discuss some of the mechanisms in different fluid models that allow for this property, and some that break it.

##### Families of mild mixing interval exchange transformations

Almost every interval exchange transformation is rigid. In this talk I will describe recent work showing that for an infinite class of permutations the set of mild mixing interval exchange transformations has full Hausdorff dimension.

##### Independent sets, local algorithms and random regular graphs

An ''ndependent set'' in a graph is a set of vertices that have no edges between them. How large can an independent set be in a random d-regular graph? How large can it be if we are to construct it using a (possibly randomized) algorithm that is local in nature? I will discuss a notion of local algorithms for combinatorial optimization problems on large, random d-regular graphs.

##### SPECIAL LECTURE: Results Related to the CR Yamabe Problem

**This is a special lecture in Geometric Analysis. Please note different day, time and location.** I will talk about the CR Yamabe problem and its related results, including the CR Yamabe flow, uniqueness and compactness of the CR Yamabe problem.

##### TBA - Tolga Etgü

##### On the spectrum of Faltings' height

The arithmetic complexity of an elliptic curve defined over a number field is naturally quantified by the (stable) Faltings height. Faltings' spectrum is the set of all possible Faltings' heights. The corresponding spectrum for the Weil height on a projective space and the Neron-Tate height of an Abelian variety is dense on a semi-infinite interval.

##### The Zakharov-Lvov stochastic model for the wave turbulence

I will discuss the stochastic model of wave turbulence, suggested in 70's by Zakharov-Lvov and present some rigorous results, concerning this theory. Next I will explain the heuristic derivation of the wave kinetic equation for the model and finally present the plan of a rigorous justification of the kinetic equation in a work under preparation with Galina Perelman.

##### Relative quantum product and open WDVV equations

The standard WDVV equations are PDEs in the potential function that generates Gromov-Witten invariants. These equations imply relations on the invariants, and sometimes allow computations thereof, as demonstrated by Kontsevich-Manin (1994). We prove analogous equations for open Gromov-Witten invariants that we defined in a previous work.

##### Superconnections and special cycles

I will start by explaining Quillen's notion of a superconnection, and then will use it to define some natural

##### The Kakeya needle problem for rectifiable sets

We show that the classical results about rotating a line segment in arbitrarily small area, and the existence of a Besicovitch and a Nikodym set hold if we replace the line segment by an arbitrary rectifiable set. This is a joint work with Alan Chang.

##### Theta functions for affine log CY varieties

Gross, Hacking, Siebert and I conjecture that the vector space of regular functions on an affine log CY (with maximal boundary) comes with a canonical basis, generalizing the monomial basis on a torus, in which the structure constants for the multiplication rule are given by counts of rational curves on the mirror.

##### Nonconvex Recovery of Low-Complexity Models

Nonconvex optimization plays important role in wide range of areas of science and engineering — from learning feature representations for visual classification, to reconstructing images in biology, medicine and astronomy, to disentangling spikes from multiple neurons. The worst case theory for nonconvex optimization is dismal: in general, even guaranteeing a local minimum is NP hard.

##### Random walk on free solvable groups

The study of free solvable groups has been advocated and pursued by Anatoly Vershik and others with various perspectives in mind. I will discuss random walks on free finitely generated solvable groups in the general context of geometric group theory and with an emphasize on exploring what algebraic properties are reflected in the behavior of various random walk.

##### Optimal regularity of three dimensional mass minimizing cones

In this talk I will present the following regularity results in minimal surface theory: the singular points of a mass minimizing three dimensional cone in the Euclidean space are contained in at most finitely many half lines (joint with C. De Lellis and L. Spolaor).

##### Classical and quantum geometric Langlands via quantization in positive characteristic

Geometric Langlands is an algebro-geometric and categorified analog of the Langlands program, introduced by A.Beilinson and V.Drinfeld. It can be understood as a certain non-commutative Fourier-Mukai transform between two moduli spaces associated to an algebraic curve and a Langlands dual pair of algebraic groups.

##### Gromov-Witten theory of locally conformally symplectic manifolds and the Fuller index

We review the classical Fuller index which is a certain rational invariant count of closed orbits of a smooth vector field, and then explain how in the case of a Reeb vector field on a contact manifold $C$, this index can be equated to a Gromov-Witten invariant counting holomorphic tori in the locally conformally symplectic manifold $C \times S^1$.

##### Remarkable identities in the counting functions for cubic and quartic rings

Let h(D) be the number of cubic rings having discriminant D, and let h'(D) be the number of cubic rings having discriminant -27D where the traces of all elements are divisible by 3. (In each case, weight rings by the reciprocal of their number of automorphisms.) At first glance, there is no relation between these two quantities, nor was there expected to be until in 1997, Y.