Title: Arithmetic and birational properties of linear spaces on intersections of two quadrics
Speaker: Lena Ji
Abstract:
In this talk, we study the lines spaces contained in the base locus of a pencil of quadrics. These encode a lot of interesting geometry: for example, for pencils of even-dimensional quadrics, there is a deep relationship between these linear spaces and hyperelliptic curves. This has found numerous applications, for example, to rational points and to moduli spaces of vector bundles. In this talk, we focus on rationality questions for the varieties of these linear spaces, especially over non-closed fields. This work is joint with Fumiaki Suzuki.
Title: A Rigid-Analytic Analogue of Artin-Grothendieck Vanishing
Speaker: Bogdan Zavyalov
Abstract: The classical Andreotti--Frankel theorem states that any Stein complex manifold $X$ has the homotopy type of a CW complex of real dimension at most dim X. Consequently, the cohomology groups H^i(X, A) vanish for any abelian group A and i > dim X. Artin and Grothendieck generalized the latter result to affine algebraic varieties, showing that for every affine variety X over an algebraically closed field k, the cohomology groups H^i(X, F) vanish for all étale torsion sheaves F and i > dim X. In this talk, I will discuss the rigid-analytic analogue of this theorem, a conjecture posed by David Hansen (and partially proven by Hansen and Bhatt–Mathew). Specifically, I will present a proof of the conjecture for affinoid rigid-analytic spaces over an algebraically closed non-archimedean field of characteristic 0 and some partial progress in characteristic p>0. This is joint work with Ofer Gabber.
Title: Moduli of surfaces fibered in log Calabi-Yau pairs
Speaker: Giovanni Inchiostro
Abstract: I will present two different compactifications of the moduli space of surfaces fibered in log Calabi-Yau pairs, coming from a generalization of quasimap theory and from KSBA-stability. This is based on a series of joint works, with Andrea Di Lorenzo; Roberto Svaldi and Junyan Zhao.