Previous Conferences & Workshops

The normal rank (or weight) of a group G is the smallest number of elements that normally generate G. This plays an important role in 3-manifold topology, but it is poorly understood. It is extremely difficult to give lower bounds apart from looking...

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 this talk, we construct a Zariski open dense locus in $M_g$ on which the Beilinson-Bloch height of the Gross-Schoen and Ceresa cycles is a Weil height, i.e. it has a lower bound and satisfies the Northcott property. This implies a...

Abstract:  Applications of o-minimality to unlikely intersection problems usually begin with the observation that the relevant analytic covering maps are definable.  However, this observation is almost never literally true in that the maps are...

Abstract: Which complex analytic spaces can arise as the universal cover of a complex algebraic variety? Motivated by this question, Shafarevich asked whether the universal cover of a smooth projective variety X is always holomorphically convex —...

Why is it so hard to prove P != NP, or even to prove super-linear circuit lower bounds? While we often blame a lack of combinatorial ingenuity, the bottleneck might be more fundamental: the logical strength of our mathematical tools.

This series of...

Abstract: Given an algebraic variety over a number field F, one can attach to it its etale cohomology groups, etale fundamental group, and higher etale homotopy groups, all equipped with an action of the absolute Galois group of F. The Galois action...

The relationship between $p$-adic (pro)-etale cohomology and de Rham cohomologies is well understood now for algebraic varieties over local fields of mixed characteristic. For analytic varieties it remains largely conjectural though much progress...

Abstract: We will discuss a proof that the integral Hodge conjecture is false for a very general abelian variety of dimension ≥ 4. Associated to any regular matroid is a degeneration of principally polarized abelian varieties. We introduce a new...