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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…

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. The main…

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…