# Number Theory & Algebraic Geometry

The Number Theory and Algebraic Geometry seminar meets on Mondays at 14:00 at room 70 in the Ross Building.
2019 Jun 17

# NT & AG Lunch: Michael Temkin "The explicit local and global class field theory"

1:00pm to 2:00pm

## Location:

Faculty lounge
I will finish the theory of Lubin-Tate, and start the last topic of this series -- Drinfeld's elliptic modules and CFT of function fields.
2019 Jun 26

# Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"

2:00pm to 4:00pm

## Location:

Ross 70
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"
2019 Jun 30

# Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"

2:00pm to 4:00pm

## Location:

Ross 70
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"
2019 Jul 01

# Minicourse: Jared Weinstein (Boston University "Geometrization of the local Langlands program"

2:00pm to 4:00pm

## Location:

Ross 70
Prof. Jared Weinstein (Boston University) will give a series of 3 talks titled "Geometrization of the local Langlands program"
2019 Jun 03

# NT & AG Seminar: Shuddhodan K V (HUJI) "Self maps of varieties over finite fields"

2:30pm to 3:30pm

## Location:

Ross building 70
Title: Title: Self maps of varieties over finite fields Abstract: Esnault and Srinivas proved that as in Betti cohomology over the complex numbers, the value of the entropy of an automorphism of a smooth proper surface over a finite field $\F_q$ is taken in the subspace spanned by algebraic cycles inside $\ell$-adic cohomology. In this talk we will discuss some analogous questions in higher dimensions motivated by their results and techniques.
2019 Jun 03

# NT & AG Lunch: Michael Temkin "The explicit local class field theory"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
I'll tell a couple of anecdotes related to imaginary quadratic fields (e.g. primes in the sequence n^2+n+41), and then open a new story -- local CFT and the explicit construction of K^ab due to Lubin-Tate.
2019 May 13

# NT & AG Lunch: Michael Temkin "Elliptic curves with complex multiplication, II"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
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 construct such an algorithm, and an independent description of a similar
2019 Jun 10

# NT & AG Seminar - Dan Edidin - An intrinsic characterization of cofree representations of reductive groups''

1:00pm to 2:00pm

## Location:

Ross 70
Title: An intrinsic characterization of cofree representations of reductive groups
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. P.S. Michael will continue his series of lectures on May 6.
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 May 06

# NT & AG Lunch: Michael Temkin "Elliptic curves with complex multiplication"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building