Events and Activities

Abstract: Since Langlands's earliest paper on his now famous program, canonical integral models of Shimura varieties have occupied a central role in modern number theory. Steady progress has been made in the intervening 50 years toward the correct...

Abstract: In 2019, Dimitrov proved the Schinzel-Zassenhaus Conjecture. Harry Schmidt and I extended his general strategy to cover some dynamical variants of this conjecture. One common tool in both results is Dubinin's Theorem on the transfinite...

Abstract: We study a non-commutative counterpart $C_n(X)$ of the symmetric product $Sym^n X$ of a space $X$, defined as the space of nxn-matrix valued points on $X$. Our main result will be a precise formula for the cohomology of this space in great...

Abstract: 
I'll start by discussing some work with Binyamini, Schmidt, and Thomas in which we prove a uniform Manin-Mumford result for products of CM elliptic curves. I'll show how we apply this to obtain an effective Andre-Oort result for fibre...

Abstract: The anabelian phenomenon may be viewed as an arithmetic analogue of Mostow rigidity: it predicts that certain varieties can be reconstructed from their arithmetic fundamental groups. A celebrated result of S. Mochizuki shows that...

Abstract: Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is...

Abstract: I will talk about a joint work with Antoine Sedillot. We study sup-norms of sections of metrized line bundles for families of arithmetic varieties. Using Riemann-Zariski spaces we obtain formulas that imply new definability results in the...