AGNT Ical Atom

A venue for invited and local speakers to present their research on topics surrounding algebraic geometry and number theory, broadly conceived. All meetings start at 14:10 sharp and end at 15:10. Meetings are held in the subterranean room -101. We expect to broadcast most meetings over Zoom at the URL https://us02web.zoom.us/j/85116542425?pwd=MzVDRmZJUVh2NXlObFVkM1N0MCt3Zz09

The seminar meets on Wednesdays, 14:10-15:10, in -101
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This Week

Mark Shusterman (Weizmann)

Fundamental Groups of Projective Varieties are Finitely Presented

Lara—Srinivas—Stix, building on joint work with Esnalut, have recently shown that the etale fundamental group of a connected proper scheme over an algebraically closed field is topologically finitely presented, thus answering a question raised in SGA. The proof relies on a finite presentation criterion of Lubotzky for profinite groups, resolutions of singularities/alterations, a theorem of Deligne—Ilusie on the Euler characteristic, as well as other modern and classical results in (arithmetic) algebraic geometry.

2023–24–B meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
May 22 Fundamental Groups of Projective Varieties are Finitely PresentedOnline Mark Shusterman (Weizmann)

Lara—Srinivas—Stix, building on joint work with Esnalut, have recently shown that the etale fundamental group of a connected proper scheme over an algebraically closed field is topologically finitely presented, thus answering a question raised in SGA. The proof relies on a finite presentation criterion of Lubotzky for profinite groups, resolutions of singularities/alterations, a theorem of Deligne—Ilusie on the Euler characteristic, as well as other modern and classical results in (arithmetic) algebraic geometry.
May 29 Supersingular elliptic curves, quaternion algebras and some applications to cryptographyOnline Eyal Goren (McGill University)

Part of the talk is expository: I will explain how supersingular isogeny graphs can be used to construct cryptographic hash functions and survey some of the rich mathematics involved. Then, with this motivation in mind, I will discuss two recent theorems by Jonathan Love and myself. The first concerns the generation of maximal orders by elements of particular norms. The second states that maximal orders of elliptic curves are determined by their theta functions.
Jun 5 TBAOnline Amnon Yekutieli (Ben Gurion University)
Jun 19 TBAOnline Francesco Maria Saettone (Ben Gurion University)
Jun 26 TBAOnline Michael Barash (Ben Gurion University)

Past Meetings

Date
Title
Speaker
Abstract
May 8 x-y duality in topological recursion, Hurwitz numbers and integrability Boris Bychkov (University of Haifa)

Topological recursion is a remarkable universal recursive procedure that has been found in many enumerative geometry problems, from combinatorics of maps, to random matrices, Gromov-Witten invariants, Hurwitz numbers, Mirzakhani’s hyperbolic volumes of moduli spaces, knot polynomials. A recursion needs an initial data: a spectral curve, and the recursion defines the sequence of invariants of that spectral curve. There is a duality in topological recursion which allows one to obtain closed formulas for the invariants of the recursion and which has implications in free probability theory and integrable hierarchies. In the talk I will survey recent progress in the topic with the examples from Hurwitz numbers theory, Hodge integrals and combinatorics of maps.

The talk is based on the joint works with A. Alexandrov, P. Dunin-Barkowski, M. Kazarian and S. Shadrin.

Seminar run by Dr. Ishai Dan-Cohen and Prof. Amnon Besser