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Given the fundamental importance of moduli spaces and their applications in many different topics, we are organizing a week long conference titled "Moduli spaces and applications in geometry, topology...
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that in nitesimal automorphis...
Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞), let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic if there exists a Green function for Δp (see [Ho1,2]); oth...
Applications of Geometric Cluster Algorithms.
The work is collaborated with Shing-Tung Yau, Feng Luo, Tony Chan, Paul Thompson, Yalin Wang, Ronald Lok Ming Lui, Hong Qin, Dimitris Samaras, Jie Gao, Arie Kaufman, and many other mathematicians, ...
Centroidal Voronoi Tessellation (CVT) is a special Voronoi tessellation in which every site xicoincides withci, the centroid of its Voronoi cellVi,CVT (left) and its corresponding Delaunay triangulati...
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfu...
Abstract: The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spec...
Abstract: We construct a complete, bounded Legendrian immersion in C^3. As direct applications of it, we show the first examples of a weakly complete bounded flat front in hyperbolic 3-space, a weakly...
We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of th...
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Con...
We prove a refined Agler decomposition for bounded analytic functions on the bidisk and show how it can be used to reprove an interesting result of Guo et al. related to extending holomorphic functio...
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a de...
By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in P4. These numbers are...
This paper deals with the computation of sectional curvature for the manifolds of N land- marks (or feature points) in D dimensions, endowed with the Riemannian metric induced by the group action of...

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