AbstractDeuring gave a classical formula for the number of supersingular elliptic curves in characteristic p. We generalize this to a formula for the cycle class of the supersingular locus in the moduli space of principally polarized abelian varieties of given dimension g. The formula determines the class up to a multiple and shows that it lies in the tautological ring. We also give the multipl...
AbstractIn an $n$-vertex graph, it is simple to see that $n$ edges imply the graph has a cycle. However, this cycle can be any length from $3$ to $n$. If we have more edges, do we get cycles of many different lengths? Can we find a cycle with some control over its length? In this talk, based on joint work with Hong Liu, I will discuss how to construct cycles of many different lengths in graphs,...