Number Theory & Algebraic Geometry

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 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.
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 Nov 05

NT&AG: Michael Temkin (HUJI), ""Differential forms on Berkovich curves"

3:00pm to 4:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
This is a continuation of the talk on October 29. After finishing a brief review of basic facts about Berkovich curves, I will associate a reduction datum to differential forms on such curves and explain how a lifting theorem for such data is proved and why it reproves the lifting theorem of [BCGGM].
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.

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