# Seminars & Events for 2016-2017

##### Weyl law for the volume spectrum

We will present our proof that the volume spectrum of a Riemannian manifold satisfies a Weyl law. This was a conjecture of Gromov. The talk is based on joint work with Liokumovich and Neves.

##### Ergodic theory and negative curvature

Ergodic theory is a very robust method to understand/distinguish dynamical systems. To a Riemannian manifold (M,g) we can associate a canonical dynamical system, its geodesic flow. During this talk we will discuss the ergodic theory of geodesic flow on negatively curved manifolds.

##### A modification of the moment method and stochastically evolving partitions at the edge

This talk is about a modification of the moment method applied to extract limiting distributions of the first, second, and so on rows of randomly evolving partitions.

##### Symmetric intersecting families

A family of sets is said to be intersecting if any two sets in the family have nonempty intersection. Families of sets subject to various intersection conditions have been studied over the last fifty years and a common feature of many of the results in the area is that the extremal families are often quite asymmetric.

##### Spanier-Whitehead $K$-duality

Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. We consider a noncommutative version, termed Spanier-Whitehead $K$-duality, which is defined on the category of $C^*$-algebras whose $K$-theory is finitely generated and that satisfy the UCT, with morphisms the Kasparov $KK$-groups.

##### Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families

We establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes. For the tame supercuspidals, we prove the limit multiplicity property with error terms. Thereby we obtain a Sato-Tate equidistribution for the Hecke eigenvalues.

##### Global Existence, Blowup and Scattering for large data Supercritical and other wave equations

**PLEASE NOTE NEW START TIME OF 3:00.** I present a new approach to classify the asymptotic behavior of certain classes of wave equations, supercritical and others, with large initial data. In some cases, as for Nirenberg type equations, a fairly complete classification of the solutions (finite time blowup or global existence and scattering) is proved.

##### Network clustering with higher order structures

Spectral clustering is a well-known way to partition a graph or network into clusters or communities with provable guarantees on the quality of the clusters. This guarantee is known as the Cheeger inequality and it holds for undirected graphs. We'll discuss a new generalization of the Cheeger inequality to higher-order structures in networks including network motifs.

##### Packaging the construction of Kuranishi structure on the moduli space of pseudo-holomorphic curve

This is a part of my joint work with Oh-Ohta-Ono and is a part of project to rewrite the whole story of virtual fundamental chain in a way easier to use. In general we can construct virtual fundamental chain on (basically all) the moduli space of pseudo-holomorphic curve. It depends on the choices.

##### Projective Dehn twist via Lagrangian cobordism

In this talk, I would like to explain my joint work with Weiwei Wu about understanding projective Dehn twist using Lagrangian cobordism.

##### Elliptic Calabi-Yau 3-folds, Jacobi forms, and derived categories

By physical considerations, Huang, Katz and Klemm conjectured in 2015 that topological string partition functions for elliptic Calabi-Yau 3-folds are governed by certain Jacobi forms. This gives strong structure results for curve counting invariants of elliptic CY 3-folds. I will explain a mathematical approach to prove (part of) the HKK Conjecture.

##### Mean field evolution of fermonic systems

**Please note different day (Wednesday), time and location (Jadwin 303). **In this talk I will discuss the dynamics of interacting fermionic systems in the mean field regime. Compared to the bosonic case, fermionic mean field scaling is naturally coupled with a semiclassical scaling, making the analysis more involved.

##### Fill-ins, extensions, scalar curvature, and quasilocal mass

There is a special relationship between the Jacobi operator and the ambient scalar curvature operator, which we'll exploit. First, I'll talk about a "cut-and-fill" technique that simplifies 3-manifolds of nonnegative scalar curvature.

##### Lefschetz Pencils

We will discuss Lefschetz pencils and will prove Lefschetz's theorem on hyperplane sections (without using transcendental methods), which will give us a more or less full understanding of the (co)homology of nonsingular complex algebraic varieties up to the middle dimension.

##### Supersymmetric approach in the random matrix theory

In this talk I will give a brief outline of the Grassmann integration technique (which is also called the supersymmetry approach) and its application to the rigorous study of main spectral characteristics of random matrices.

##### From Integrability to Medical Imaging and to the Asymtotics of the Riemann Zeta Function

It is often realized that this technique can actually be used for the solution of a plethora of other problems,and thus it becomes a mathematical method.In this lecture, a review will be presented of how a concrete problem in the area of integrability led to the development of a new method in mathematical physics for analyzing boundary value problems for linear and for integrable nonlinear PDEs

##### Complexity-separating graph classes for vertex, edge and total colouring

Given a class A of graphs and a decision problem X belonging to NP, we say that a full complexity dichotomy of A was obtained if one describes a partition of A into subclasses such that X is classified as polynomial or NP-complete when restricted to each subclass.

##### Conway mutation and knot Floer homology

Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair.

##### The Unpolarized Shafarevich Conjecture for K3 Surfaces

Shafarevich made the following conjecture for higher genus curves: the set of isomorphism classes of genus g curves over K (a number field) with good reduction outside S (a fixed finite set of primes) is finite. Faltings proved this and the analogous conjecture for abelian varieties of given degree. Zarhin proved this finiteness across all degrees.

##### Generated Jacobian equations and regularity: optimal transport, geometric optics, and beyond

**PLEASE NOTE SPECIAL DAY, TIME AND LOCATION. **Equations of Monge-Amp{\`e}re type arise in numerous contexts, and solutions often exhibit very subtle properties; due to the highly nonlinear nature of the equation, and its degenerate ellipticity.