Number Theory & Algebraic Geometry

2019 May 13

NT & AG Seminar: "A dream desingularization algorithm", Michael Temkin (HU)

2:30pm to 4:00pm

Location: 

Ross 70
Abstract: Any birational geometer would agree that the best algorithm
for resolution of singularities should run by defining a simple invariant of
the singularity and iteratively blowing up its maximality locus.
The only problem is that already the famous example of Whitney umbrella
shows that this is impossible, and all methods following Hironaka had
to use some history and resulted in more complicated algorithms.
Nevertheless, in a recent work with Abramovich and Wlodarczyk we did
2019 May 27

NT & AG Seminar "A dream desingularization algorithm", Michael Temkin

2:30pm to 3:30pm

Abstract: Any birational geometer would agree that the best algorithm for resolution of singularities should run by defining a simple invariant of the singularity and iteratively blowing up its maximality locus. The only problem is that already the famous example of Whitney umbrella shows that this is impossible, and all methods following Hironaka had to use some history and resulted in more complicated algorithms. Nevertheless, in a recent work with Abramovich and Wlodarczyk we did construct such an algorithm, and an independent description of a similar
2019 Apr 15

NT & AG Lunch: Yakov Varshavsky "Geometric class field theory"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
In a series of 2 talks I will try to explain that in the function field case the unramified global class
field theory has a simple geometric interpretation and a conceptual proof. We will only consider the unramified case (see, for example, https://arxiv.org/pdf/1507.00104.pdf or https://dspace.library.uu.nl/handle/1874/206061)
Key words: Abel-Jacobi map, l-adic sheaves, sheaf-function correspondence.
2019 Apr 29

NT & AG Lunch: Yakov Varshavsky "Geometric class field theory, II"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building

Geometric class field theory is an analog of the classical class field theory over function fields in which functions are replaced by sheaves. In the first part of my talk, I will formulate the result and explain its proof over C (the field of complex numbers).  

In the  second part of the talk, I will try to outline the proof in the case of finite fields and indicate how this result implies the classical unramified global class field theory over function fields. 

Most of the talk will be independent of the first one. 
2019 May 20

Landau Lecture 2: Old and new on the de Rham-Witt complex (NT - AG Seminar)

Lecturer: 

Prof. Luc Illusie (Université Paris-Sud)
2:30pm to 3:30pm

Location: 

Ross 70

Old and new on the de Rham-Witt complex

Abstract: After reviewing the definition and the basic properties of the de Rham-Witt complex for smooth schemes over a perfect field, I will discuss the new approach to the subject developed by Bhatt, Lurie and Mathew.

I will explain the main results and sketch work in progress on the problems raised by this theory.

2019 Apr 08

NT & AG Seminar - Daniel Disegni

2:30pm to 3:30pm

Location: 

Ross 70A

Title: p-adic equidistribution of CM points on modular curves
Abstract: Let X be a modular curve. It is a curve over the integers, whose complex points form a quotient of the upper half-plane by a subgroup of SL(2,Z). In X there is a natural supply of algebraic points called CM points. After an idea of Heegner, they can be used to construct rational points on elliptic curves.
2019 Apr 08

NT & AG Lunch: Michael Temkin, "Explicit Class Field Theory"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building

In a series of talks I will describe in the chronological order all cases where an explicit
construction of CFT is known:
0. The multiplicative group and Kronecker-Weber -- the case of Q.
1. Elliptic curves with complex multiplication and
Kronecker's Jugendraum -- the case of imaginary quadratic extensions.
2. Formal O-models of Lubin-Tate -- the local case.
3. Drinfeld's elliptic modules -- the function field case.
\infinity. Extending this to real quadratic fields and, more generally,
2019 Apr 01

NT & AG Lunch: Ehud DeShalit "An overview of class field theory, III"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
Class field theory classifies abelian extensions of local and global fields
in terms of groups constructed from the base. We shall survey the main results of class
field theory for number fields and function fields alike. The goal of these introductory lectures
is to prepare the ground for the study of explicit class field theory in the function field case,
via Drinfeld modules.
I will talk for the first 2 or 3 times.
2019 Mar 25

NT & AG Lunch: Ehud DeShalit "An overview of class field theory, II"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
Class field theory classifies abelian extensions of local and global fields
in terms of groups constructed from the base. We shall survey the main results of class
field theory for number fields and function fields alike. The goal of these introductory lectures
is to prepare the ground for the study of explicit class field theory in the function field case,
via Drinfeld modules.
I will talk for the first 2 or 3 times.
2019 Mar 18

NT & AG Lunch: Ehud DeShalit "An overview of class field theory"

1:00pm to 2:00pm

Location: 

Faculty lounge, Math building
Class field theory classifies abelian extensions of local and global fields
in terms of groups constructed from the base. We shall survey the main results of class
field theory for number fields and function fields alike. The goal of these introductory lectures
is to prepare the ground for the study of explicit class field theory in the function field case,
via Drinfeld modules.
I will talk for the first 2 or 3 times.
2019 Mar 18

NT & AG - Antoine Ducros (Sorbonne Université), "Non-standard analysis and non-archimedean geometry"

2:30pm to 3:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
There is a general slogan according to which the limit behaviour of a one-parameter family of complex algebraic varieties when the parameter t tends to zero should be (partially) encoded in the associated t-adic analytic space in the sense of Berkovich; this slogan has given rise to deep and fascinating conjecturs by Konsevich and Soibelman, as well as positive results by various authors (Berkovich, Nicaise, Boucksom, Jonsson...).
2018 Dec 17

NT & AG - Sazzad Biswas

2:30pm to 3:30pm

Location: 

Ross 70

Title: Local root numbers for Heisenberg representations 


Abstract: On the Langlands program, explicit computation of the local root numbers 
(or epsilon factors) for Galois representations is an integral part.
But for arbitrary Galois representation of higher dimension, we do not
have explicit formula for local root numbers. In our recent work
(joint with Ernst-Wilhelm Zink) we consider Heisenberg representation
(i.e., it represents commutators by scalar matrices) of the Weil

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