Past Events

Framed instanton Floer homology was constructed by Kronheimer and Mrowka, and has become a useful invariants for 3-manifolds. It has a closed relation with the representation variety of the fundamental group of the 3-manifolds. However, many basic structures and tools are…

We study the scaling of the one-arm exponent in near-critical but subcritical percolation in high-dimensional percolation, extending a famous result of Kozma and Nachmias at the critical point. As a key tool, we derive a sharpening of existing half-plane two-point function bounds. As a…

Abstract:  We will discuss the following results: If f: X -> P1 is a morphism of smooth projective varieties over the complex numbers with at most a single singular fibre, then X is chain uniruled by sections of f.  The same conclusion holds, but with genus zero multisections…

Abstract: Igusa varieties are smooth varieties in characteristic p arising naturally as étale covers of certain subvarieties (central leaves) of Shimura varieties, for example of the ordinary locus of the modular curve. Igusa varieties over the (mu)-ordinary locus of a Shimura variety are used…

Abstract: We consider the long time behavior of the solutions to the Burgers-Fisher-KPP equation. This equation exhibits a transition from the pulled (a la FKPP)  to the pushed (a la Allen-Cahn) behavior at a critical value $\beta_c$ of the strength of the Burgers term.…

Introduction to random graphs

Given a compact Lie group G acting on a space X, the G-equivariant elliptic cohomology of X is naturally a scheme Ell_G(X) (with a map down to the moduli space of G-bundles on elliptic curves). Given a G-equivariant vector bundle V on X, one obtains an interesting line bundle Thom(V) on Ell_G(X…

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