The HUJI-BGU-Zoom Workshop in Arithmetic

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The HUJI-BGU-Zoom 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).



4th meeting: Monday and Wednesday, June 29 and July 1st, 2020 - Zoom


The two days will be dedicated to talks by students on a topic related to their current or future research.

Zoom Meeting ID: 919 4923 6705
Password: 679062

Link:https://huji.zoom.us/j/91949236705?pwd=M011UEVXczZudlVEaE9KOVNFMEpLUT09

Schedule:

Monday June 29:
14:00-- Francesco Saettone (BGU), Lubin-Tate formal groups

Wednesday July 1:
14:30-- Ido Karshon (HUJI), Elliptic curves have infinitely many primes of supersingular reduction
15:15-- Yotam Svoray (BGU), On the global equivalence class of discriminants of ordinary transversal type singularities
16:00-- Arnon Hod (BGU), Action of local groups of Lie type on basic affine space and intertwining operators




Abstracts of talks

Francesco Saettone
Motivated by an analogy with the theory of complex multiplication on elliptic curves, Lubin and Tate showed in 1965 how formal groups over local fields can be used to deduce several foundational theorems of local class field theory, beginning by explicitly describing the maximal abelian extension K^ab of a local field K. Lubin-Tate formal groups can be also used to construct the Artin map, named after a similar construction for the global case by Emil Artin. The Artin map gives an isomorphism between the subgroup Gal(K^ab/K^ur) and the integral units of the local field K.

Ido Karshon (14:30-15:00)
Elliptic curves over finite fields come in two flavors, ordinary and supersingular. In the 1980's Elkies proved that for any elliptic curve E over Q, there are infinitely many primes p such that E is supersingular when reduced modulo p. We will give definitions, motivate the problem, and sketch his short but tricky proof.

Yotam Svoray (15:15-15:50)
Turning smooth objects over C into singular objects in many cases simplifies the object but also preserves many geometric properties. A natural question to ask is how do neighborhoods of the singular points look like, and does it matter which singular point we choose? More specifically, if the singular locus of X is non-isolated, then what can we say about how X looks around the different points of Sing(X)? In this talk we will discuss a subscheme called "the transversal discriminant" in the case where X is a hypersurface, which lets us understand properties regarding the transversality of Sing(X). We will see that it is in fact a Cartier divisor and that we can compute its equivalence class in Pic(Sing(X)), and show how this helps us compute a bound on the jumps of multiplicity in Sing(X).

Arnon Hod (16:00-16:30)
The study of representation theory is the understanding of as much symmetry as possible on a given vector space. We will study the space of square integrable functions on a two dimensional vector space over a p-adic field. By noting group actions on this space we present a decomposition of this space. Some of the group actions we present can be chosen in a non-unique way. We present a theorem classifying all such group actions.



Dates to be saved

TBA


Past meetings

3rd meeting, March 30th, 2020 (Zoom)
2nd meeting, January 13th, 2020 (BGU)
 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.
Zoom: www.zoom.us

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.)