Welcome to Geometry in Istanbul II. This 1-day event is the second iteration of our gathering (following Geometry in Istanbul I), bringing together researchers and mathematicians to discuss recent developments in geometry and related fields.
Speakers & Abstracts
Yuri Prokhorov
Steklov Mathematical Institute of RAS & HSE University
Title: Tetragonal conic bundles
Abstract: We will discuss the birational geometry of three-dimensional algebraic varieties with a conic bundle structure. In particular, it will be shown that the dimension of the linear system \(|2K_S+C|\) is a birational invariant in the category of such varieties (possibly modulo a finite number of families).
The talk is based on a joint work with V.V. Shokurov.
Yuri Tschinkel
New York University (Courant Institute) & Simons Foundation
Title: Invariants in equivariant birational geometry
Abstract: I will discuss new ideas and constructions in equivariant birational geometry (joint with A. Kresch).
Ivan Cheltsov
University of Edinburgh
Title: G-birationally rigid cubic threefolds
Abstract: A Fano variety X equipped with an action of a group G is called G-birationally rigid if X is a G-Mori fibred space (over a point) and X is not G-birational to any other G-Mori fibre space. In this talk I will classify all pairs (X,G) consisting of a (possibly singular) cubic threefold X and a subgroup G of its automorphism group such that X is G-birationally rigid.
Oliver Bültel
Boğaziçi University
Title: Shimura varieties modulo p with many compact factors
Abstract: We give several new moduli interpretations of the fibers of certain Shimura varieties over several prime numbers. As a consequence one obtains that for every prescribed odd prime characteristic p every bounded symmetric domain possesses quotients by arithmetic groups whose models have good reduction at a prime divisor of p.
Sinan Ünver
Koç University
Title: The Infinitesimal Dilogarithm
Abstract: Polylogarithms appear in many branches of mathematics: as regulators in number theory, algebraic geometry and K-theory; in expressing scattering amplitudes in mathematical physics and volumes of hyperbolic manifolds; and in the theory of cluster algebras.
I will give an infinitesimal version of polylogarithms and in the case of weight two (the dilogarithm case), explain how these functions give regulators from K-theory, infinitesimal invariants of algebraic cycles and a proof of an infinitesimal version of Goncharov's strong reciprocity conjecture.