Number Theory & Algebraic Geometry

2018 Oct 29

NT & AG Lunch: Yakov Varshavsky "Class Field Theory"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
The goal of my talk will be to introduce the local and the global
the Class field theory. Though definitions of all basic objects
(inverse limits, p-adic numbers, adeles, ideles, etc.) will be briefly recalled,
it is recommended that the participants review these notions
before the lecture.
The talk will be independent of the first lecture
2018 Nov 05

NT & AG Lunch: Yakov Varshavsky "Global class field theory".

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
The main goal of my talk will be to introduce adeles and ideles and to formulate the global class
field theory both for number fields and function fields.
Key words: adeles, ideles, class field theory, algebraic curves.
2018 Oct 22

NT & AG Lunch: Jasmin Matz "Modular forms"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
Abstract: Modular forms are historically the first example of automorphic
forms, and are still studied today as they have many applications. In
this talk I want to introduce modular forms, give some examples, and, if
time permits, explain the connection to elliptic curves, objects we
already met in the first lecture.
2018 Oct 15

NT & AG Lunch: Yakov Varshavsky "Mathematics around Langlands program"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building

This is a new seminar, whose official name is "Topics in number theory
and algebraic geometry". At least in the beginning the goal
of the seminar will be to give a (relatively) gentle introduction to
various topics, which should be accessible to beginning but motivated graduate students.
The seminar has a number in the shnaton (80942), so graduate students
can get a credit for it.
First talk: The goal of this organizational/introductory talk will be to
describe areas of mathematics, connected to Langlands program.
2018 Dec 31

NT&AG: Eyal Subag (Penn State University), "Symmetries of the hydrogen atom and algebraic families"

2:30pm to 3:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.
2018 Jun 25

NT&AG: Gal Porat (HUJI), "Induction and Restriction of $(\varphi,\Gamma)$-Modules"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Abstract. Let L be a non-archimedean local field of characteristic 0. In this talk we will present a variant of the theory of (\varphi,\Gamma)-modules associated with Lubin-Tate groups, developed by Kisin and Ren, in which we replace the Lubin-Tate tower by the maximal abelian extension \Gamma=Gal (L^ab/L). This variation allows us to compute the functors of induction and restriction for (\varphi,\Gamma)-modules, when the ground field L changes. If time permits, we will also discuss the Cherbonnier-Colmez theorem on overconvergence in our setting.
Joint work with Ehud de Shalit.
2018 Jun 11

NT&AG: Peng Xu (HUJI), "Supersingular representations of unramifed $U(2,1)$"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
The recent work of Abe--Henniart--Herzig--Vigneras gives a classification of irreducible admissible mod-$p$ representations of a $p$-adic reductive group in terms of supersingular representations. However, supersingular representations remain mysterious largely, and in general we know them very little. Up to date, there are only a classification of them for the group $GL_2 (Q_p)$ and a few other closely related cases.
2018 Jun 04

NT&AG: Hillel Firstenberg (HUJI), "Hyper-modular functions, irrationality of \zeta(3), and algebraic functions over finite fields"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Using formal power series one can define, over any field, a class of functions including algebraic and classical modular functions over C. Under simple conditions the power series will have coefficients in a subring of the field - say Z - and this plays a role in Apery's proof of the irrationality of \zeta(3). Remarkably over a finite field all such functions/power series are algebraic.
I will call attention to a natural - but open - problem in this area.
2018 Jan 21

NT&AG: Daniel Disegni (University of Paris-Sud 11), On the p-adic Bloch-Kato conjecture for Hilbert modular forms

3:00pm to 4:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
The Birch and Swinnerton-Dyer conjecture predicts that the group of rational points on an elliptic curve E over Q has rank equal to the order of vanishing of the L-function of E. Generalisations of this conjecture to motives M were formulated by Belinson and Bloch-Kato. I will explain a proof of a version of the Bloch-Kato conjecture in p-adic coefficients, when M is attached to a p-ordinary Hilbert modular form of any weight and the order of vanishing is 1.
2015 Nov 09

Number theory: Ishai Dan-Cohen (Essen), "Towards Chabauty-Kim loci for the polylogarithmic quotient over an arbitrary number field"

4:00pm to 5:45pm

Location: 

Ross Building, room 70, Jerusalem, Israel
Title: Towards Chabauty-Kim loci for the polylogarithmic quotient over an arbitrary number field
Abstract: Let K be a number field and let S be an open
subscheme of Spec O_K.
Minhyong Kim has developed a method for
bounding the set of S-valued points on a
hyperbolic curve X over S; his method opens
a new avenue in the quest for an "effective
Mordell conjecture".
But although Kim's approach has lead to the
construction of explicit bounds in special
cases, the problem of realizing the potential
2015 Dec 07

Number theory: Jean-Baptiste Teyssier (HUJI) "Kedlaya-Mochizuki theorem and applications"

4:00pm to 5:15pm

Location: 

Ross Building, room 70A
Let X be a complex manifold and let M be a meromorphic connection on X with
poles along a normal crossing divisor D. Levelt-Turrittin theorem asserts that the pull-back of M to the formal neighbourhood of a codimension 1 point in D decom poses (after ramification) into elementary factors easy to work with.
This decomposition may not hold at some other points of D. When it does, we say
that M has good formal decomposition along D. A conjecture of Sabbah, recently
proved by Kedlaya and Mochizuki independently, asserts roughly the
2018 Jan 29

NT&AG: Shachar Carmeli (Weizmann Institute), "Higher Etale Obstructions for Quadratic Forms"

2:00pm to 3:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Higher Etale obstructions are cohomological obstructions introduced by Yonatan Harpaz and Tomer Schlank for solutions of algebraic equations over a field. Their definition is based on the theory of relative etale homotopy type. In my talk I will explain the construction of relative etale homotopy type and the resulting obstruction theory.
I will also present the calculation of these obstructions for quadratic equations of the form a_1x_1^2 + ... + a_nx_n^2 = 1. This is a joint work with Edo Arad and Tomer Schlank.

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