The HUJI-BGU Workshop in Arithmetic
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.
Schedule
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)
TBA
Ishai Dan-Cohen (16.00-16.15)
TBA
Dates to be saved
TBA
Past meetings
1st meeting, December 16th, 2019
(HUJI)
Locations
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.)