# Seminars & Events for 2015-2016

##### On Erdos-Ko-Rado for random hypergraphs

One of the more interesting of recent combinatorial directions has been the attempt to understand the extent to which various classical facts remain true in a random setting. The present talk will mostly discuss what we know about this question when the ``classical fact" is the Erdos-Ko-Rado Theorem.

##### From local class field theory to the curve and vice versa

I will speak about results contained in my article "G-torseurs en théorie de Hodge p-adique" linked to local class field theory. I will in particular explain the computation of the Brauer group of the curve and why its fundamental class is the one from local class field theory.

##### An index theorem for CR manifolds with S^{1} action

**Please note special day, location and time. **

##### Floer homology for translated points

**PLEASE NOTE: THIS SEMINAR WILL BE HELD AT COLUMBIA UNIVERSITY IN ROOM MATH 520. **A point q in a contact manifold (M,ξ) is said to be a translated point of a contactomorphism ϕ, with respect to a contact form α for ξ, if it is a "fixed point modulo the Reeb flow", i.e. if q and ϕ(q) are in the same Reeb orbit and ϕ preserves α at q.

##### Functors and relations from Fukaya categories of LG models

**PLEASE NOTE: THIS SEMINAR WILL BE HELD AT COLUMBIA UNIVERSITY IN ROOM MATH 407. **The Fukaya category of a Landau-Ginzburg (LG) model W: E --> C, denoted F(E,W), enlarges the Fukaya category of E to include certain non-compact Lagrangians determined by W (for instance, Lefschetz fibrations and their thimbles).

##### $L^2$ invariants and Benjamini-Schramm convergence

Does there exist a sequence of free subgroups $F_k$ of the isometry group of hyperbolic $n$-space such that the Cheeger constant of the quotient space $H^n/F_k$ tends to zero as $k$ tends to infinity? I will explain how to answer this (and related questions) when $n$ is even using a curious result of $G$.

##### Bounds on eigenvalues on riemannian manifolds

##### Ricci solitons

**Please note special time (4:15). **We discuss the asymptotic geometry of complete noncompact four dimensional shrinking Ricci solitons and outline a program for their classification.

##### Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway

Please see the conference webpage at http://math.arizona.edu/~grouptheory/princeton/ for more information.

#### Schedule of talks:

**Monday, November 2**

##### Negative and positive results in the intersection between systolic and symplectic geometry

How small is the smallest period of a closed trajectory of a Reeb flow? In this talk I will present recent answers to instances of this question in three-dimensions which reveal connections between systolic and symplectic geometry. I will present results both of a positive and of a negative nature.

##### Positivity of the complex Neumann Laplacian

In this talk we will discuss aspects of spectral theory of the complex Neumann Laplacian in several complex variables. In particular, we will discuss geometric and potential theoretic characterizations of positivity and spectral discreteness of the complex Neumann Laplacian.

##### Min-max, phase transitions and minimal hypersurfaces

**Please note special time. **There is a strong correspondence between critical points of in the theory of phase transitions and critical points of the area functional in theory of minimal hypersurfaces. Historically, research has focused in studying the case of minima or stable critical points.

##### A New Analytic Approach to Wave Turbulence

In this talk we discuss improvements to a new approach to wave turbulence instigated by Zaher Hani, Pierre Germain and Erwan Faou. This approach will combine techniques from analytic number theory and dispersive PDE theory to study an example of discrete turbulence, for which dynamics is dominated by the exact resonances of the equation.

##### Lecture I: Geometry and dynamics on hyperbolic surfaces

The first lecture will give some background on the geometry and dynamics on hyperbolic surfaces. I will give a brief overview of Teichm\"uller theory and properties of the mapping class groups and the space of geodesic currents. I will discuss some natural actions of the mapping class group. I will formulate some basic questions and explain some of the ideas used for studying these objects.

##### An Axiomatic Foundation for Non-Bayesian Learning in Networks

Rational learning postulates that individuals incorporate new information into their beliefs in a Bayesian fashion. Despite its theoretical appeal, this Bayesian learning framework has been criticized on the basis of placing unrealistic computational demands on the agents.

##### On the Moy-Prasad filtration and supercuspidal representations

Reeder and Yu gave recently a new construction of certain supercuspidal representations of p-adic reductive groups (called epipelagic representations). Their construction relies on the existence of stable vectors in the first Moy-Prasad filtration quotient under the action of a reductive quotient.

##### Hyperplane Arrangements and Stopping Times

**Please note special day (Tuesday, November 10). ** Consider a real hyperplane arrangement and let C denote the collection of the occuring chambers.

##### Local eigenvalue statistics for random regular graphs

I will discuss results on local eigenvalue statistics for uniform random regular graphs. Under mild growth assumptions on the degree, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics (gap statistics and averaged energy correlation functions) are given by those of the GOE. Joint work with J. Huang, A. Knowles, and H.-T. Yau.

##### Effective Matsusaka's theorem for surfaces in characteristic p

The goal of this talk is to explain how to obtain an effective version of Matsusaka's theorem for arbitrary smooth algebraic surfaces in positive characteristic. It provides an effective bound on the multiple which makes an ample line bundle very ample. The proof is based on a Reider-type analysis of adjoint linear series combined with bend and break techniques