# Seminars & Events for 2011-2012

##### Large Time Behavior of Periodic Viscosity Solutions of Integro-differential Equations

In this talk, I will present some recent results on the asymptotic behavior of periodic viscosity solutions of parabolic integro-differential equations (where nonlocal terms are associated with Levy-It\^o operators). In particular, we address the problem to mixed integro-differential equations, e.g.

##### Ramussen's s-Invariant via Instantons and Other Remarks on Khovanov Homology as Seen by Instanton Floer Homology

##### Nonlocal Evolution Equations

Nonlocal evolution equations have been around for a long time, but in recent years there have been some nice new developments.

##### Nonlocal Evolution Equations

Nonlocal evolution equations have been around for a long time, but in recent years there have been some nice new developments.

##### Bertini theorems for F-singularities

I will discuss Bertini theorems for F-singularities ( i.e. singularities defined by Frobenius); the proof is based on a slight generalization of Cumino-Greco-Manaresi's axiomatic approach to Bertini theorems. This is a joint work with Karl Schwede.

##### Universal conductivity in graphene; some rigorous results and open problems

Recent experiments have found an universal value for the dynamic conductivity in graphene, fully confirming theoretical predictions based on a non interacting tight binding model. This however poses a problem since one could expect a many body renormalization of the non interacting value of the conductivity due to the interaction.

##### Some applications of almost mathematics

I will try to explain how, by inserting the word "almost" in appropriate places in a commutative algebra textbook and using the fact that $\mathbb{Q}_p$ an $\mathbb{F}_p((t))$ have the same residue field, Faltings gave a new proof of a result of Fontaine and Wintenberger relating the absolute Galois groups of these two fields.

##### On Sidorenko's Conjecture

The Erdos-Simonovits-Sidorenko conjecture is well-known in combinatorics but it has equivalent formulations in analysis and probability theory. The shortest formulation is an integral inequality related to Mayer integrals in statistical mechanics and Feynman integrals in quantum field theory. We present new progress in the area. Part of the talk is based on joint results with J.L. Xiang Li.

##### The Jones polynomial and surfaces far from fibers

This talk explores relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement.

##### The Jones polynomial and surfaces far from fibers

This talk explores relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement.

##### Weights in a Serre-type conjecture for U(3)

We consider a generalisation of Serre's conjecture for irreducible, conjugate self-dual Galois representations rho : $G_F -> GL_3(\bar F_p)$, where $F$ is an imaginary quadratic field in which $p$ splits. We previously gave a conjecture for the possible Serre weights of rho.

##### Bihermitian metrics and Poisson deformations

A bihermitian metric (or generalized Kahler structure) involves a pair of complex structures and a metric compatible with both. The study of these is closely related to that of holomorphic Poisson structures on a manifold.

##### Vinogradov estimates applied to maximal theorems related to Waring's problem

I'll discuss the discrete spherical maximal function of Magyar--Stein--Wainger and it's estimates. Then I'll prove recent results for higher degrees which use Vinogradov type estimates for exponential sums to improve results about maximal functions defined on the hypersurfaces arising in Waring's problem.

##### Varieties fibered by good minimal models

Let $f:X->Y$ be an algebraic fiber space such that the general fiber has a good minimal model. We show that if $f$ is the Iitaka fibration then $X$ has a good minimal model. The result reduces the minimal model conjecture to the case of varieties of Kodaira dimension zero and the non-vanishing conjecture.

##### Crossing probabilities, their densities, and modular forms

A crossing probability is the probability of finding a critical cluster that touches specified boundary arcs.

##### Global Stability Results for Relativistic Fluids in Expanding Spacetimes

In this talk, I will discuss the future-global nonlinear behavior of relativistic fluids evolving in expanding spacetimes. I will focus on how the global behavior of the fluid is affected by both the spacetime expansion rate and the fluid equation of state.

##### Theta Constant Identities on $Z_n$ Curves

In this talk we shall expose a concrete relation between the algebraic and transcendental parameters of a nonsingular $z_n$ curve.

##### Subspace evasive sets

We describe an explicit, simple, construction of large subsets of F^n, where F is a finite field, that have small intersection with every k-dimensional affine subspace.

##### Mapping class groups of Heegaard splittings

The mapping class group of a Heegaard splitting for a given 3-manifold is the group of automorphisms of the 3-manifold that take the Heegaard surface onto itself, modulo isotopies that preserve the surface setwise. This can be viewed as a subgroup of the mapping class group of the surface.

##### Spectral factors in endoscopic transfer

This talk is based on some results for real groups used in Arthur's classification of global packets for classical groups. The setting is twisted endoscopy for a connected reductive algebraic group over the reals. There is a geometric transfer which generates useful test functions on the real points of an endoscopic group.