# Seminars & Events for 2013-2014

##### The structure of graphs with no cycles of length divisible by three

For a graph G, let #E(G) be the number of stable sets of even size and let #O(G) be the number of stable sets of odd size. We are interested in the relation between the structure of a graph and the value of |#E(G)-#O(G)|.

##### Fluid models from plasma physics

we will give an overview of some (charged) fluid models from plasma physics, mainly introducing the models and stating some important results and open questions.

##### There are finitely many surgeries in Perelman's Ricci flow

Although the Ricci flow with surgery has been used by Perelman to solve the Poincaré and Geometrization Conjectures, some of its basic properties are still unknown. For example it has been an open question whether the surgeries eventually stop to occur (i.e.

##### The characteristic gluing problem for the wave equation and applications

We will first describe the characteristic gluing problem for the wave equation on a general four-dimensional Lorentzian manifold. We will show that the only obstruction to such gluing constructions is in fact the existence of certain ``conservation laws'' on null hypersurfaces and we will then obtain necessary and sufficient conditions for the existence of such conservation laws.

##### (Deterministic) Communication Amid Uncertainty

The classical theory of communication assumes perfect coordination between sender and receiver of information, to develop a beautiful mathematical theory that ensures reliable efficient communication. Natural communication, for example, between humans, is however characterized by a lack of perfect agreement among the communicating players.

##### TBA - Lieblich

##### New limiting distributions for the Moebius function

In this talk, we will present some new limiting theorems for a family of signed distributions on square-free numbers. These distributions arise naturally from the study of the Moebius function and allowed us to prove "signed" versions of the Erdos-Kac theorem.

##### On k-regular maps

The question about the existence of a continuous k-regular map from a topological space X to an N-dimensional Euclidean space R^N, which would map any k distinct points in X to linearly independent vectors in R^N, was first considered by Borsuk in 1957.

##### Three-coloring graphs with no induced 6-edge paths

Since graph-coloring is an NP-complete problem in general, it is natural to ask how the complexity changes if the input graph is known not to contain a certain induced subgraph H. Results of Kaminski and Lozin, and Hoyler, show that the problem remains NP-complete unless H is a disjoint union of paths.

##### Of logarithms and exponents: convection at infinite Prandtl numbers with mixed thermal boundary conditions

For decades, experiments (and more recently numerical simulations) have attempted to determine how the effective transport of heat (measured by the non-dimensional Nusselt number Nu) scales with the driving force (as measured by the Rayleigh number Ra) --when said driving force is asymptotically strong--in Rayleigh-Benard convection where an incompressible, Boussinesq fluid is driven by an impo

##### Equivariant maps from a configuration space to a sphere

THIS IS A JOINT TOPOLOGY/ALGEBRAIC TOPOLOGY SEMINAR. PLEASE NOTE DIFFERENT TIME AND LOCATION. There are several distinct reasons to ask for the existence of an S_n-equivariant map from the configuration space F(R^d,n) of n labeled points in R^d to a certain S_n-representation sphere of dimension (d+1)(n-1)-1. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Equivariant maps from a configuration space to a sphere

THIS IS A JOINT TOPOLOGY/ALGEBRAIC TOPOLOGY SEMINAR. There are several distinct reasons to ask for the existence of an S_n-equivariant map from the configuration space F(R^d,n) of n labeled points in R^d to a certain S_n-representation sphere of dimension (d+1)(n-1)-1. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Optimal transport and regularity of c-convex potentials

The question of regularity in optimal transport and related equations of Monge Ampere type has seen a lot of activity in the past few decades. Starting from the usual quadratic cost in R^n and now ranging

##### Beyond the Borsuk-Ulam/Dold theorem (in Combinatorial Geometry)

**THIS IS A SPECIAL ALGEBRAIC TOPOLOGY SEMINAR. PLEASE NOTE DIFFERENT DATE, TIME AND LOCATION. **In this talk we present an evolution of equivariant topology methods in Combinatorial Geometry.

##### Random weighted Sobolev inequalities

We extend a randomisation method, introduced by Burq-Lebeau on compact manifolds, to the case of the harmonic oscillator. We construct measures, under concentration of measure type assumptions, on the support of which we prove optimal weighted Sobolev estimates on R^d.

##### Living on the edge: A geometric theory of phase transitions in convex optimization

Recent empirical research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the l1 minimization method for identifying a sparse vector from random linear samples.

##### On the moduli space of quintic surfaces

We describe the use of GIT and stable replacement for studying the geometry of a special compactification of the moduli space of smooth quintic surfaces, the KSBA compactification. In particular we discuss the interplay between non-log-canonical singularities and boundary divisors.

##### Distribution of primes in arithmetic progressions with application

We discuss the recent developments on the distribution of primes in arithmetic progressions which are regarded as stronger versions of the Bombieri-Vinogradov theorem. First we explain why the arguments based on the dispersion method, Fourier analysis and Kloosterman sums make it possible to obtain mean value results for arithmetic prgressions to moduli beyond x1=2.

##### Moments of the Riemann Zeta Function

An important area of study in analytic number theory is the average behaviour of the Riemann zeta function on the critical line Re(s) = 1/2. I'll talk a bit about what we know so far, and how random matrix theory helps us predict even more. If time permits, I'll discuss how one can generalise this to the average behaviour of families of L-functions at the critical point s = 1/2.

##### GIT and μ-GIT

**Please note different day and time. **In this lecture I will explain the moment-weight inequality, and its role in the proof of the Hilbert-Mumford numerical criterion for μ-stability. The setting is Hamiltonian group actions on closed Kaehler manifolds.