• 2018 May 03

Colloquium - Dvoretzki lecture 1: Alexei Borodin (MIT) - 'Integrable probability'

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The goal of the talk is to survey the emerging field of integrable probability, whose goal is to identify and analyze exactly solvable probabilistic models. The models and results are often easy to describe, yet difficult to find, and they carry essential information about broad universality classes of stochastic processes.
• 2018 Apr 26

Colloquium: Zabrodsky lectures - Camillo De Lellis (University of Zurich) - "The oriented Plateau problem and a question of Almgren"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
• 2018 Apr 12

Colloquium: Ron Peretz (Bar Ilan) - "Repeated Games with Bounded Memory - the Entropy Method"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract:
In the past two decades the entropy method has been successfully employed in the study of repeated games. I will present a few results that demonstrate the relations between entropy and memory. More specifically: a finite game is repeated (finitely or infinitely) many times. Each player $i$ is restricted to strategies that can recall only the last $k_i$ stages of history. The goal is to characterize the (asymptotic) set of equilibrium payoffs. Such a characterization is available for two-player games, but not for three players or more.
Related papers:
• 2018 Mar 22

Colloquium: Gilles Zemor (Université de Bordeaux) - "Additive Combinatorics in Field Extensions"

3:30pm to 4:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Additive combinatorics enable one to characterize subsets S of elements in a group such that S+S has small cardinality. We are interested in linear analogues of these results, namely characterizing subspaces S in some algebras (mostly extension fields) such that the linear span of the set S^2 of products st, for s,t in S, has small dimension. We shall present a linear analogue of a theorem of Vosper which says that under the right conditions, a sufficiently small dimension for S^2 implies that S has a basis of elements in geometric progression.
• 2018 Jan 25

Ostrowski Prize Lecture - Akshay Venkatesh (Stanford) - Period maps and Diophantine problems

2:15pm to 3:45pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a family of complex algebraic varieties parameterized by a base variety B there is an associated period mapping, which (at least locally) goes from B to a certain flag variety. However, although both the source and target are algebraic varieties,
this period map is of a transcendental nature.
I will explain joint work with Brian Lawrence which shows how the transcendence of the period mapping
• 2018 Jan 18

Colloquium: Menachem Magidor (HUJI) - "Can the continuum problem can be solved?"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The Continuum Problem is whether there is a set of reals whose cardinality is strictly between the cardinality of the integers and the reals.
• 2018 Jan 11

Colloquium: Andrei Okounkov (Columbia) - "Catching monodromy"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Monodromy of linear differential and difference equations is a very old and classical object, which may be seen as a far-reaching generalization of the exponential map of a Lie group. While general properties of this map may studied abstractly, for certain very special equations of interest in enumerative geometry, representation theory, and also mathematical physics, it is possible to describe the monodromy "explicitly", in certain geometric and algebraic terms. I will explain one such recent set of ideas, following joint work with M. Aganagic and R. Bezrukavnikov.
• 2018 Jan 04

Colloquium: Joachim König (Universität Würzburg) - "Specialization of Galois coverings over number fields"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The inverse Galois problem (over number fields k) is one of the central problems in algebraic number theory. A classical approach to it is via specialization of Galois coverings: Hilbert’s irreducibility theorem guarantees the existence of infinitely many specialization values in k such that the Galois group of the specialization equals the Galois group of the covering. I will consider problems related to the inverse Galois problem which can be attacked using the specialization approach.
• 2017 Dec 28

Colloquium: Or Hershkovits (Stanford) - "The Mean Curvature flow and its applications"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Being the gradient flow of the area functional, the mean curvature flow can be thought of as a greedy algorithm for simplifying embedded shapes. But how successful is this algorithm?
In this talk, I will describe three examples for how mean curvature flow, as well as its variants and weak solutions, can be used to achieve this desired simplification.
The first is a short time smoothing effect of the flow, allowing to smooth out some rough, potentially fractal initial data.
• 2017 Dec 21

Colloquium: Alex Lubotzky (HUJI) - "Groups approximation, stability and high dimensional expanders"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Several well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)?
In the case of U(n), the question can be asked with respect to different metrics andnorms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which arenot approximated by U(n) with respect to the Frobenius (=L_2) norm.