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.
Schedule
| Time |
Event / Title |
Speaker |
| 09:30 – 10:00 |
Arrival |
|
| 10:00 – 11:00 |
Talk 1: Tetragonal conic bundles |
Yuri Prokhorov |
| 11:00 – 11:15 |
Short Break |
|
| 11:15 – 12:15 |
Talk 2: Invariants in equivariant birational geometry |
Yuri Tschinkel |
| 12:15 – 13:30 |
Lunch |
|
| 13:30 – 14:30 |
Talk 3: Wall-crossing invariant combinations of Welschinger numbers for rational surfaces |
Sergey Finashin |
| 14:30 – 15:00 |
Coffee Break |
|
| 15:00 – 16:00 |
Talk 4: Shimura varieties modulo p with many compact factors |
Oliver Bültel |
| 16:00 – 16:15 |
Short Break |
|
| 16:15 – 17:15 |
Talk 5: The Infinitesimal Dilogarithm |
Sinan Ünver |
Abstracts
Yuri Prokhorov
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).
Sergey Finashin
Middle East Technical University
Title: Wall-crossing invariant combinations of Welschinger numbers for rational surfaces
Abstract: (Joint with V.Kharlamov) We refine the real enumerative invariants not sensitive to changing the real structure that we elaborated in our previous paper for del Pezzo
surfaces, and extend these refined invariants to arbitrary rational surfaces.
The definition requires a choice of an auxiliary conic bundle and of a Pin- structure.
We prove independence of our invariants of these choices and provide
recursive relations for computing these invariants.
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.