# Seminars & Events for 2012-2013

##### Contact Non-Squeezing and Rabinowitz Floer Homology

We will present joint work with Will Merry. Using spectral invariants in Rabinowitz Floer homology we present an abstract contact non-squeezing theorem for periodic contact manifolds. We then exemplify this in concrete examples. Finally we explain connections to the existence of a biinvariant metric on contactomorphism groups.

##### Embedded constant mean curvature surfaces in Euclidean three space

Constant mean curvature (CMC) surfaces are critical points to the area functional with an enclosed volume constraint. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Global dynamics beyond the ground state for the energy critical Schrodinger equation

##### What is a degree distribution?

The most studied aspect of statistical network models is their degree structure, reflecting the propensity of nodes within a network to form connections with other nodes. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### A divisor with non-closed diminished base locus

I will explain the construction of a pseudoeffective **R**-divisor *Dλ* on the blow-up of * P3* at nine very general points which has negative intersections with an infinite set of curves, whose union is Zariski dense.

##### Quantum Information Functionals

Quantum information functionals and their algebraic properties play an important role in quantum information theory. Recent developments in the theory of operator monotone and operator convex functions and related topics have simplified earlier results and also led to new insights. One example is the convexity of chi-square divergences.

##### Hidden structures in large matrices

Consider the problem of estimating the entries of a large matrix, when most of the entries are either hidden from us or blurred by noise. Of course, one needs to assume that the matrix has some structure for this estimation to be possible. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### The Gauss-Bonnet Theorem

The Gauss-Bonnet Theorem states that a certain integral of a two-dimensional Riemannian manifold's curvature is equal to the manifold's Euler characteristic. I shall prove this theorem in three (or maybe more) ways, using three different definitions of curvature, and three different definitions of the Euler characteristic. But are these "really" all the same definition? And are these "really

##### Entropy and the localization of eigenfunctions on negatively curved manifolds - II

We are interested in the behaviour of laplacian eigenfunctions on negatively curved manifolds, in the high frequency limit. The Quantum Unique Ergodicity conjecture predicts that they should become uniformly distributed over phase space, and the Shnirelman theorem states that this is true if we allow ourselves to possibly drop a ``negligible'' family of eigenfunctions.

##### Wedge operations and torus symmetries

A fundamental result of toric geometry is that there is a bijection between toric varieties and fans. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Discrepancy of graphs and hypergraphs

How uniformly is it possible to distribute edges in a graph? For instance, is there a graph of density 1/2 in which every induced subgraph has approximately the same number of edges as nonedges?

##### Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci

I will report on the construction of p-integral models of various algebraic compactifications of PEL-type Shimura varieties and Kuga families, allowing ramification (including deep levels) at p, with good behaviors over the loci where certain (multiplicative) ordinary level structures are defined. (We know almost nothing about the non-ordinary loci when p is ramified, but this theory is still

##### Root systems of torus graphs and automorphism groups of torus manifolds

A torus manifold is a compact oriented 2n-dimensional T^n-manifold with fixed points. We can define a labelled graph from given torus manifold as follows: vertices are fixed points; edges are invariant 2-spheres; edges are labelled by tangential representations around fixed points. THIS IS A JOINT TOPOLOGY / ALGEBRAIC TOPOLOGY SEMINAR.

##### Symplectic cohomology and loop homology

The string topology of Chas-Sullivan produces operations on the homology of the free loop space of orientable manifolds, and analogous structures are known to exist on the symplectic cohomology of their cotangent bundles. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### On equations with drift and diffusion.

An drift-diffusion equation is like the heat equation with an extra first order term. In some cases, the Laplacian is replaced by a fractional Laplacian. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Algebraic Geometry of K-stability and its application to Moduli varieties

K-stability is a stability for varieties (Tian, Donaldson), a modification of classical stability (Mumford). While it has been known for several decades that classically stability does not work in higher dimensions moduli construction, the author explains how the K-stability fits into recent construction of compact moduli of general type varieties by KSBA (Koll\'ar-Shepherd-Barron, Alexeev) theory. CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

(PLEASE NOTE SPECIAL DAY AND TIME.)

##### The Boltzmann equation, Besov spaces, and optimal decay rates in R^n

In this talk, we will study the large-time convergence to the global Maxwellian of perturbative classical solutions to the Boltzmann equation on R^n, for n geq 3, without the angular cut-off assumption. We prove convergence of the k-th order derivatives in the norm L^r_x(L^2_v), for any 2 leq r leq infinity, with optimal decay rates, in the sense that they are equal to the rates which one obtains for the corresponding linear equation. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Physical Reproduction of Materials with Specified Reflectance and Scattering

Although real-world surfaces can exhibit significant variation in materials - glossy, diffuse, metallic, translucent, etc. - printers are usually used to reproduce color or gray-scale images. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### Big cycles and volume functions

The volume of a divisor is an important invariant measuring the "positivity" of its numerical class. I will discuss an analogous construction for cycles of arbitrary codimension. In particular, this yields geometric characterizations of big cycle classes modeled on the well-known criteria for divisor and curve classes.

##### Hydrodynamic turbulence as a problem in non-equilibrium statistical mechanics

The problem of hydrodynamic turbulence is reformulated as a heat flow problem along a chain of mechanical systems which describe units of fluid of smaller and smaller spatial extent. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.