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Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
An important discovery of the 20th century mathematics is that many deterministic systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal...
Abstract: We introduce techniques for turning estimates on the infinitesimal behavior of solutions to nonlinear equations (statements concerning tangent cones and blow ups) into more effective control...
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 investigate Lp regularity of weighted Bergman projec-tions and zeros of weighted Bergman kernels for the weights that are radially symmetric and comparable to 1 on the unit disc.

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