2018 Nov 19

# NT&AG: Gaku Liu (Max Planck Institute of Mathematics), "Semistable reduction in characteristic 0"

2:30pm to 4:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
We address the semistable reduction conjecture of Abramovich and Karu: we prove that every surjective morphism of complex projective varieties can be modified to a semistable one. The key ingredient is a combinatorial result on triangulating lattice Cayley polytopes. Joint work with Karim Adiprasito and Michael Temkin. The lecture consists of two parts: first 30 minutes an algebra-geometric introduction by Michael Temkin, and then a one hour talk by Gaku Liu about the key combinatorial result.
2018 Nov 20

# Dynamics Lunch: Jiange Li "Sumsets and entropy" after Ruzsa

12:00pm to 1:00pm

## Location:

Manchester faculty club
2018 Dec 05

# Logic Seminar - Omer Ben-Neria

11:00am to 1:00pm

## Location:

Ross 63

Hjorth's theory of turbulence

The purpose of this talk is to survey several results from Hjorth's theory of turbulent polish group actions.

We will start by discussing certain classification problems associated with Borel equivalence relations, and present the notions of Borel reductions and smooth relations, and the E_0 dichotomy theorem of Harrington-Kechris-Louveau.

2018 Nov 14

# Logic Seminar - Yair Hayut

11:00am to 1:00pm

## Location:

Ross 63

Global Chang's Conjecture

Yair Hayut - (joint with Monroe Eskew)

For $\kappa < \lambda$ infinite cardinals let us consider the following generalization of the Lowenheim-Skolem theorem:
"For every algebra with countably many operations over $\lambda^+$ there is a sub-algebra with order type exactly $\kappa^+$".

We will discuss the consistency and inconsistency of some global versions of this statement and present some open questions.
2018 Dec 19

# Logic Seminar - Udi Hrushovski

11:00am to 1:00pm

## Location:

Ross 63

Model theory and geometry of fields with automorphism

I will review some of the model-theoretic geometry of difference varieties, and some open problems.
A difference variety is defined by polynomial equations with an additional operator $\si$ interpreted as a field automorphism.
2018 Dec 17

# NT & AG Lunch: Jasmin Matz "Automorphic L-functions I"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Abstract: The goal of this (and the next) talk is to introduce automorphic L-functions for GL(n) and other split groups, and to discuss some of their properties and some conjectures. Key words: L-functions, Langlands dual group, modular forms
2018 Dec 03

# NT & AG Lunch: Yakov Varshavsky Title: "GL(n,F)\GL(n,A)/GL(n,O) over function fields and vector bundles on curves"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Abstract: The starting point of the geometric approach to the theory of automorphic forms over function fields is a beautiful observation of Weil asserting that there is a natural bijection between the two-sided quotient GL(n,F)\GL(n,A)/GL(n,O) and the set of isomorphism classes rank n vector bundles on a curve. The goal of my talk will be to explain this result and to give some applications. Key words: adeles and ideles in the function field case, algebraic curves, line and vector bundles on curves, Picard group, Riemann-Roch theorem.
2019 Jan 07

# NT & AG Lunch: Yakov Varshavsky "Algebraic stacks, II"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Last week we discussed what does it means for a functor to be a "sheaf" in the etale topology. Our goal now will be to complete the definition of algebraic stacks and to give examples. Key words: algebraic stacks, faithfully flat morphisms, faithfully flat descent, moduli spaces of vector bundles on curves.
2018 Dec 31

# NT & AG Lunch: Yakov Varshavsky "Algebraic stacks"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
The main goal of this talk will be to define algebraic stacks and to give examples. Our main example will be moduli "space" of vector bundles on a smooth projective curve. Key words: groupoids, Grothendieck topologies, etale and smooth morphisms of schemes, G-torsors, algebraic stacks.
2018 Dec 24

# NT & AG Lunch: Jasmin Matz "Automorphic L-functions II"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Having defined the standard automorphic L-function for GL(n) in the first talk, we now proceed to the definition of L-functions for general split groups and representations of the Langlands dual group (which will be discussed as well). I then want to discuss some results and conjectures regarding these L-functions. Key words: L-functions, Langlands dual group, modular forms
2018 Dec 10

# NT & AG Lunch: Yakov Varshavsky "Introduction to algebraic stacks"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Abstract: The goal of this talk will be to explain what are algebraic stacks and why they naturally appear. If time permits, we will start discussing our main example of moduli spaces of vector bundles on a smooth projective curve. Key words: groupoids, Grothendieck topologies, etale and smooth morphisms of schemes, algebraic stacks.
2018 Nov 26

# NT & AG Lunch: Sazzad Biswas "Local factors, and converse problems"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Title: Local (L-, \epsilon- and \gamma-) factors, and converse theorems. Abstract: Our first goal will be to define local (L-,\epsilon- and \gamma-) factors and to study their properties. These factors are needed to formulate the local Langlands correspondence for GL(n), which was outlined two weeks ago. We will do it first for supercuspidal representations of GL(n) and then for local Galois representations, that is, for representations of Gal(\bar{F}/F), where F is a local field.
2018 Nov 19

# NT & AG Lunch: Sazzad Biswas "Local gamma factors, and converse problems"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
Let F be a non-Archimedean local field. In the representation theory of GL_n(F), one of the basic problems is to characterize its irreducible representations up to isomorphism. There are many invariants (e.g., epsilon factors, L-functions, gamma factors, depth, etc) that we can attach to a representation of GL_n(F). Roughly, the local converse problem is to find the smallest subcollection of twisted local \gamma-factors which classifies the irreducible admissible representations of GL_n(F) up to isomorphism.
2019 Jan 14

# NT & AG Lunch: Yakov Varshavsky "Moduli "spaces" of vector bundles on curves"

1:00pm to 2:00pm

## Location:

Faculty lounge, Math building
First we am going to recall first basic facts about vector bundles on smooth projective curves. Then we will talk about moduli "spaces" of vector bundles on curves. If time permits, we will also talk about related "spaces" like Hecke stacks and moduli "spaces" of shtukas. Key words: Riemann-Roth theorem for curves, vector bundles on curves, degree.
2019 Jan 08

# Dynamics Lunch: Nachi Avraham Re'em: "Sethuraman-Varadhan's Proof of the Central Limit Theorem for Non-Homogeneous Markov Chains"

12:00pm to 1:00pm