# Events & Seminars

# Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".

## Location:

A family of problems in Diophantine geometry has the following

form: We fix a collection of "special" algebraic varieties among which the

0-dimensional are called "special points". Mostly, if V is a special variety

then the special points are Zariski dense in V, and the problem is to prove

the converse: If V is an irreducible algebraic variety and the special

points are Zariski dense in V then V itself is special.

Particular cases of the above are the Manin-Mumford conjecture Read more about Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".

# Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".

## Location:

A family of problems in Diophantine geometry has the following

form: We fix a collection of "special" algebraic varieties among which the

0-dimensional are called "special points". Mostly, if V is a special variety

then the special points are Zariski dense in V, and the problem is to prove

the converse: If V is an irreducible algebraic variety and the special

points are Zariski dense in V then V itself is special.

Particular cases of the above are the Manin-Mumford conjecture Read more about Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".

# Logic Seminar - Chen Meiri

## Location:

The model theory of higher rank arithmetic groups

**Abstract:**In this talk we will present joint work with Nir Avni and Alex Lubotzky concerning the model theory of higher rank arithmetic groups. We will show that many of these groups are determined by their first order theory as individual groups and also as a collection of groups.

# Basic Notions: Ari Shnidman "Randomness in arithmetic: class groups."

## Location:

For everynumber field K, there is a finite abelian group C called the

class group, which serves as an obstruction to unique factorization.

Since Gauss, number theorists have tried to understand questions such

as how often is C trivial, or how often C contains an element of fixed

order (as K varies). In the 1970's, Cohen and Lenstra observed

empirically that when the degree and signature of K is fixed, the

isomorphism class of C adheres to a natural probability distribution.

I'll discuss these Cohen-Lenstra heuristics and survey what is known, Read more about Basic Notions: Ari Shnidman "Randomness in arithmetic: class groups."

# AG & NT lunch: Gil Livneh "Purely Inseparable Galois Morphisms and Smooth Foliations"

Abstract: Inseparable extensions and morphisms are an important feature in positive characteristic. The study of these uses (smooth) foliations in the tangent bundle of derivations, as was first seen in a theorem of Jacobson (1944) on purely inseparable field extensions of exponent 1. In this talk we will state Jacobson's theorem and some of its generalizations: to normal domains, to regular local and non-local rings, and to morphisms of smooth varieties.

# Logic Seminar - Mark Kamsma

## Location:

**Kim-independence in positive logic**

# Dynamics lunch: Daren Wei (HUJI) - Loosely Bernoulli, non-loosely Bernoulli and horocycle flows

# Amitsur Algebra seminar: Daniele Dona (HUJI)

## Location:

Speaker: Daniele Dona (HUJI)

Title: Towards a CFSG-free diameter bound for Alt(n).

# Basic Notions: David Kazhdan "On the Langlands conjecture for curves over local fields."

## Location:

In this talk I present conjectures and results of joint work with Pavel Etingof and Edward Frenkel on an analytic version of the Langlands correspondence for curves over local fields.

Zoom link:

https://huji.zoom.us/j/87131022302?pwd=SnRwSFRDNXZ4QVFKSnJ1Wit2cjZtdz09

# Analysis seminar (SPECIAL TIME): Yuri Lvovsky (HUJI) — Bounded multiplicity of eigenvalues of the vibrating clamped circular plate

It was shown by C. L. Siegel (1929) that the eigenvalues of the vibrating membrane problem has no non-trivial multiplicities. In this talk we consider the eigenvalues of the vibrating clamped plate problem. This is a fourth order problem. We show that its eigenvalues

have multiplicity at most six. The proof is based on a new recursion formula for

a Bessel-like function and on Siegel-Shidlovskii Theory.

If time permits we also consider the problem of determining the density of the

nodal sets of a clamped plate.

# Amitsur algebra seminar: Eilidh McKemmie (HUJI)

## Location:

__Speaker:__Eilidh McKemmie

__Title__: The probability of generating invariably a finite simple group

__Abstract__: We say a group is invariably generated by a subset if every tuple in the product of conjugacy classes of elements in that subset is a generating tuple.

We discuss the history of computational Galois theory and probabilistic generation problems to motivate some results about the probability of generating invariably a finite simple group. We also highlight some methods for studying probabilistic invariable generation.