Baltimore-Washington
Metro Area Differential Geometry Seminar

The following speakers are confirmed:

Arnaud Debussche (ENS, Rennes, France)

Title: Stochastic nonlinear Schroedinger equations

Abstract:

The nonlinear Schroedinger equation is a prototype model to describe propagation of waves in dispersive media. It arises in several modelisation and noise appears naturally. It may represent the noise due to amplifiers or random dispersion in the fiber. In this talk I will present some aspects of well-posedness and influence on blow-up phenomena for the stochastic nonlinear Schroedinger.

Or Hershkovits (Stanford University)

Title: The topology of self-shrinkers and sharp entropy bounds.

Abstract:

The Gaussian entropy, introduced by Colding and Minicozzi, is a rigid motion and scaling invariant functional which measures the complexity of hypersurfaces of the Euclidean space. It is defined to be the supremal Gaussian area of all dilations and translations of the hypeprsurface, and as such, is well adapted to be studied by mean curvature flow. In the case of the n-th sphere in R^{n+1}, the entropy can be computed explicitly, and is decreasing as a function of the dimension n.

A few years ago, Colding Ilmanen Minicozzi and White proved that all closed, smooth self-shrinking solutions of the MCF have larger entropy than the entropy of the n-th sphere. In this talk, I will describe a generalization of this result, which derives better (sharp) entropy bounds under topological constraints. More precisely, we show that if M is any closed self-shrinker in R^{n+1} with a non-vanishing k-th homotopy group (with k\leq n), then its entropy is higher than the entropy of the k-th sphere in R^{k+1}.

This is a joint work with Brian White.

Szymon Plis (Cracow University of Technology)

Title: Pluripotential theory on almost complex surfaces

Abstract:

I will present a short overview of the theory of plurisubharmonic functions on almost complex manifolds. Then I will discuss proper- ties of the Monge-Amp`ere operator for plurisubharmonic functions on almost complex surcaces (i.e. almost complex manifolds which have real dimention four) and present some applications.

Lei Ni (UC San Diego)

Title: Metric characterizations of the projectivity

Abstract:

Recently there were several progresses on the algebraic and analytic properties of Kaehler manifolds in terms of holomorphic sectional curvature. In this talk I shall discuss some new joint results (with Fangyang Zheng) along these directions. The result either generalizes the existing one or provides a complementary coverage. The new curvature conditions also opens many questions.