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2021 Jan 14

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

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4:00pm to 5:15pm

Location: 

Zoom

 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

2021 Jan 07

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

Read more >
4:00pm to 5:15pm

Location: 

Zoom

 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

2020 Dec 23

Logic Seminar - Chen Meiri

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10:50am to 12:35pm

Location: 

https://huji.zoom.us/j/82821066522?pwd=aVJnTkxBYktycHdzNFN5WDV0R2FkZz09

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. 
2020 Dec 31

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

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4:00pm to 5:15pm

Location: 

Zoom

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,

2020 Dec 21

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

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1:00pm to 2:00pm


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.
2020 Dec 22

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

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12:00pm to 1:00pm

Abstract: We will concentrate on two papers by Marina Ratner: "Horocycle flows are loosely Bernoulli". Israel J. Math. 31 (1978) no. 2, 122-132. and "The Cartesian square of the horocycle flow is not loosely Bernoulli". Israel J. Math. 34 (1979). , no. 1-2, 72-96 (1980). We will start from the definition of loosely Bernoulli, then a detailed discussion about the proof that horocycle flow is loosely Bernoulli and finally some hints about the non-loosely Bernoulli proof in the product case.
2020 Dec 09

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

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11:00am to 12:00pm


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.
2020 Dec 10

Amitsur algebra seminar: Eilidh McKemmie (HUJI)

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12:00pm to 1:00pm

Location: 

https://huji.zoom.us/j/83390879904?pwd=RlpVblJHUzQ0SlIxL24vcEZjU3BjZz09


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.
2020 Dec 07

AG & NT Lunch: Zev Rosengarten "Unipotent groups over imperfect fields"

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1:00pm to 2:00pm

Abstract: Unipotent groups form one of the fundamental building blocks in the theory of linear algebraic groups. Over perfect fields, their behavior is very simple. But over imperfect fields, the situation is much more complicated. We will discuss various aspects of these groups, from the fundamental theory to a study of their Picard groups, which appear to play a central role in understanding their behavior. 










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