The HUJI-BGU Workshop in Arithmetic

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The HUJI-BGU Workshop in Arithmetic meets twice a semester, alternating locations, starting from the year 5780. All are welcome.
The workshop is currently organized by Ari Shnidman (HUJI) and Daniel Disegni (BGU).

2nd meeting: Monday January 13th, 2020 - BGU

The theme of the day will be L-functions of characters, and the arithmetic significance of their special values.

All talks will be in Building 58, room -101 (please be careful of sign mistakes)
10.30 - 11.00 Welcome and coffee
11.00 - 11:50 Francesco M. Saettone (BGU), Analytic continuation of L-functions of characters: Tate's thesis.
12.05 - 12.55 Zev Rosengarten (HUJI), L-functions of characters and regulators: Beilinson's conjecture.

14.15 - 15.05 Amnon Besser (BGU), The p-adic Beilinson conjectures for number fields.
15.20 -16.00 Yotam Svoray (BGU), Polylogarithms and their geometry.
16.00 -16.15 (bonus content): Ishai Dan-Cohen (BGU) Regulators are polylogarithms.

Abstracts of talks

Francesco M. Saettone (11.00-11.50)
John Tate in his PhD thesis (Princeton 1950) reproved the functional equation and the analytic continuation of Hecke L-functions. By class field theory, which I will recall, those are L-functions of characters of Galois group. Tate's new proof consists in an innovative use of adelic integration, i.e., Fourier analysis on the adeles: after a quick review of fundamental tools from harmonic analysis, I will introduce the main results of the adelic machinery (adeles and ideles, strong approximation theorem, idele class group) and how they have been used in the study of local and global zeta functions. This approach gives a more conceptually clarifying point of view on Hecke's result (1920).

Zev Rosengarten (12.05-12.55)
The classical class number formula relates the residue of the zeta function of a number field to the regulator of the group of units. Similarly, the Birch and Swinnerton-Dyer Conjecture relates the value of the L-function of an elliptic curve to a "regulator," namely the period of the N\'eron differential along a real cycle. These conjectures found a common generalization in work of Deligne, and ultimately, Beilinson, who formulated a general conjecture relating special L-values to regulators of period maps. We will discuss this conjecture, providing examples along the way, and then sketch Beilinson's proof of his conjecture for 0-dimensional abelian motives over Q (which is just a fancy way of saying Dirichlet characters).

Amnon Besser (14.15-15.05)
I will begin by explaining the general philosophy, due to Perrin-Riou, of p-adic Beilinson conjectures. I will then explain how one can test this conjecture numerically for totally real Artin motives using an explicit description of K-theory of fields and the p-adic polylogarithm.

Yotam Svoray (15.20-16.00)

Ishai Dan-Cohen (16.00-16.15)

Dates to be saved


Past meetings

1st meeting, December 16th, 2019 (HUJI)


HUJI: Einstein Institute of Mathematics, Hebrew University Giv'at Ram Campus, Jerusalem.
BGU: Deichmann Building for Mathematics (building 58), Ben-Gurion University of the Negev, Be'er Sheva.

Directions: you may use Google Maps or Moovit. (Please note that Google is sometimes optimistic about the travel time of local buses.)