Grad Colloquium: James Lee

Abelian varieties are higher-dimensional analogues of elliptic curves and play a central role in modern algebraic geometry and number theory. In layman's terms, they are projective varieties that have a group structure. When working over a field of positive characteristic p, the geometry of an abelian variety is influenced in interesting ways by the prime p. It is analogous to how fields of characteristic p > 0 admit inseparable field extensions and have a lot of exotic phenomena. Consequently, there is a class of invariants, called p-invariants, that can be assigned to abelian varieties over characteristic p, and a current research topic is studying which invariants are possible. In particular, one can look at the stratifications induced by the invariants and study whether they have nice geometric properties such as irreducibility, smoothness, etc.