The HUJI-BGU-Zoom Workshop in
The HUJI-BGU Workshop in Arithmetic meets semiregularly,
alternating locations save for pandemics etc., starting from the
year 5780. All are welcome.
The workshop is currently organized by Ari Shnidman
(HUJI) and Daniel
5th meeting: Monday, June 27th, 2022 - HUJI
Schedule: (all talks in Ross 70, Givat Ram)
10.15-10.40 Welcome (in Manchester building faculty lounge)
Abstracts of talks
10.45-12.00 Eran Assaf (Dartmouth), Definite orthogonal
13.30-14.45 Ishai Dan-Cohen (BGU), A motivic Weil height
machine for curves
(link to watch live
15.15-16.30 Ari Shnidman (HUJI), Explicit counterexamples to the local-to-global principle
(link to watch live
Eran Assaf (10.45-12.00)
We consider spaces of modular forms attached to positive definite
quadratic forms in four variables, and make explicit their
connection to Hilbert modular forms using the even
Clifford functor. By relating it to the theory of theta lifts
we obtain an explicit theta correspondence, and gain a full
understanding of the systems of Hecke eigenvalues that can
arise. We will discuss further applications to non-vanishing
and Eisenstein congruences, and touch upon the picture in higher
This is joint work with Dan Fretwell, Colin Ingalls, Adam Logan,
Spencer Secord and John Voight.
Ishai Dan-Cohen (13.30-14.45)
The rational points of a smooth curve over a number field map to the
set of augmentations of the associated motivic algebra. An
expectation, closely related to Kim's conjecture, is that the set of
augmentations which are locally geometric is equal to the set of
rational points. We provide evidence for this expectation by
extending aspects of the "Weil height machine" to the set of locally
geometric augmentations. This is ongoing joint work with L.
Ari Shnidman (15.15-16.30)
Selmer showed that the cubic plane curve 3x^3 + 4y^3 + 5z^3 = 0 has no rational
points over Q but has points everywhere locally (i.e. over each Q_p).
It therefore gives an element of order 3 in the Tate-Shafarevich group Sha(E) of
a certain elliptic curve E. It is still not known whether for every prime p there
exists an elliptic curve E over Q with elements of order p in Sha(E). In work with
Ariel Weiss last year, we showed that for each prime p, there exist simple abelian varieties
A over Q with elements of order p in Sha(A). In this talk, I'll discuss recent work with
Victor Flynn, which shows that the p-part of Sha(A) can in fact be arbitrarily large.
Moreover, we construct the torsors violating the local-to-global principle explicitly, as mu_p-covers
of Jacobians of superelliptic curves.
Dates to be saved
4th meeting, June 29th-July 1st, 2020
3rd meeting, March 30th,
2nd meeting, January 13th, 2020 (BGU)
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 to the physical locations: you may use Google Maps
or Moovit. (Please note that Google is sometimes optimistic about
the travel time of local buses.)