# Seminars & Events for 2009-2010

##### Periodicity and Duality

This talk will produce periodic families of Poincare duality spaces, giving a partial answer to a problem posed in the proceedings of the 1982 Northwestern homotopy theory conference. The ideas will also relate James Periodicity to the four-fold periodicity of the surgery obstruction groups.

##### Bundle structures and Algebraic K-theory

This talk will describe (Waldhausen type) algebraic K-theoretic obstructions to lifting fibrations to fiber bundles having compact smooth/topological manifold fibers.The surprise will be that a lift can often be found in the topological case. Examples will be given realizing the obstructions.

##### An effective proof of the Oppenheim Conjecture

In the mid 80's Margulis proved the Oppenheim Conjecture regarding values of indefinite quadratic forms. I will present new work, joint with Margulis, where we quantify this statement by giving bounds on the size of integer vectors for which $|Q(x)|<\epsilon$ for an irrational indefinite quadratic form $Q$ in three variables.

##### Diophantine Properties of Dynamical Systems and IETs

The lecture is based on a recent preprint with the same title, joint with J. Chaika and put recently on arXiv. One of the results is that for ergodic IETs (Interval Exchange Transformations) almost sure $\liminf_{n\to\infty} n|T^nx-y|=0$.

##### Uniqueness of constant scalar curvature Kähler metrics

We will show that constant scalar curvature Kähler(cscK) metric "adjacent" to a given Kähler class is unique up to isomorphism. This generalizes the previous uniqueness theorems of Chen-Tian and Donaldson, where the complex structure is fixed. Joint work with X-X. Chen.

##### Radiation field for Einstein Vacuum equations

##### Ideas around Symplectic Field Theory

Symplectic Field Theory (SFT) is the study of (pseudo-)holomorphic curves in symplectic cobordisms and contains Gromov-Witten theory and symplectic Floer theory as special cases. The algebraic invariants of SFT are obtained by a simultaneous study of infinitely many interdependent first order elliptic systems which exhibit compactness and transversality issues.

##### The k edge-disjoint paths problem in digraphs with bounded independence number

In 1980, Fortune, Hopcroft, and Wyllie showed that the following algorithmic problem (k-EDP) is NP-complete with $k=2$: k Edge-Disjoint Paths (k-EDP) Instance: A digraph $G$, and $k$ pairs $(s_1,t_1),...,(s_k,t_k)$ of vertices of $G$.

Question: Do there exist directed paths $P_1,...,P_k$ of $G$, mutually edge-disjoint, such that $P_i$ is from $s_i$ to $t_i$ for $i=1,...,k$?

##### Bordered Floer homology and factoring mapping classes

I will discuss "bordered Floer homology", an invariant for three-manifolds with parameterized boundary. The theory associates a differential graded algebra to a (parameterized) surface; and a module over that algebra to a three-manifold which bounded by the surface.

##### A Phase transition for a model of Random band matrices

Miniconference on Dynamical Systems at Princeton

##### Zero temperature limits of Gibbs states

Miniconference on Dynamical Systems at Princeton

##### Escape rates and variational principles for dynamical systems with holes

Miniconference on Dynamical Systems at Princeton

##### Progress on Affine Sieves

Miniconference on Dynamical Systems at Princeton

##### The Mobius function, randomness and dynamics

Miniconference on Dynamical Systems at Princeton

##### The Full Renormalization Horseshoe for Unicritical Maps, revisited

Miniconference on Dynamical Systems at Princeton

##### Geometry and Topology of Chaotic Transport

Miniconference on Dynamical Systems at Princeton

##### On Arnold diffusion in arbitrary degrees of freedom and an almost dense orbit on energy surface

Miniconference on Dynamical Systems at Princeton

##### Ergodicity of some open systems with particle-disk interactions

Miniconference on Dynamical Systems at Princeton

##### Lyapunov exponents, periodic orbits and horseshoes in infinite dimensional systems

Miniconference on Dynamical Systems at Princeton

##### Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes equations

Miniconference on Dynamical Systems at Princeton