Past Events

In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical...

A famous congruence equation question is the solvability of x y = c (mod q) with x, y in intervals of length q^{1/2 + epsilon}. In this talk, we will discuss its history and recent developments. We will show that it is solvable for almost all pairs...

In [Mazur, Visualizing elements of order three in the Shafarevich-Tate group, Asian J. Math. 3 (1999), no. 1, 221-232], Mazur proves that any element in Sha[3](E/K) can be made visible in an abelian surface. Mazur did not comment on whether this...

Almost twenty years ago, the celebrated theorem of Witten-Kontsevich asserted that the intersection theory of Deligne-Mumford space is governed by KdV-hierarchies. Around the same time, Witten proposed a sweeping generalization which leads to the...

The loop-erased random walk Y^n is the process obtained by running a random walk in Z^d from the origin to the first exit time of the ball of radius n and then chronologically erasing its loops. If we let X_n denote the number of steps of Y^n then...

In this joint work with Albert Chau and Weiyong He, we prove existence of longtime smooth solution to mean curvature flow of entire Lagrangian graphs without assuming curvature bounds on initial manifold. We also obtain a Bernstein type result for...

I will discuss the Hrushovski-Kazhdan integration theory, which is a major development in the theory of motivic integration. I will first present the fundamental constructions in this theory (homomorphisms between various Grothendieck rings). Then i...

A new family of mixed finite element methods for the Stokes and incompressible Navier-Stokes equations is presented. It is inf-sup stable and consistent, such that arbistrarily high order approximations can be achieved by increasing the polynomial...

Consider a vector bundle E of rank k over a finite CW complex X. Assume k>dimX for simplicity. If E is not trivial, then it will contain various trivial sub-bundles of maximal rank r. The geometric dimension of E is simply defined to be gd(E)=k-r. It...