Colloquium

  • 2018 May 17

    Colloquium - Tzafriri lecture: Amitay Kamber (Hebrew university) "Almost-Diameter of Quotient Spaces and Density Theorems"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    A recent result of Lubetzky and Peres showed that the random walk on a $q+1$-regular Ramanujan graph has $L^{1}$-cutoff, and that its “almost-diameter” is optimal. Similar optimal results were proven by other authors in various contexts, e.g. Parzanchevski-Sarnak for Golden Gates and Ghosh-Gorodnik-Nevo for Diophantine approximations. Those results rely in general on a naive Ramanujan conjecture, which is either very hard, unknown, or even false in some situations. We show that a general version of those results can be proven using the density hypothesis of Sarnak-Xue.
  • 2018 May 10

    Colloquium: Zemer Kosloff (Hebrew University) - "Poisson point processes, suspensions and local diffeomprhisms of the real line"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    The study of the representations theoretic properties of the group of diffeormorphisms of locally compact non compact Riemmanian manifolds which equal to the identity outside a compact set is is linked to a natural quasi invariant action of the group which moves all points of a Poisson point process according to the diffeomorphism (Gelfand-Graev-Vershik and Goldin et al.).
    Neretin noticed that the local diffeomorphism group is a subgroup of a larger group which he called GMS and that GMS also acts in a similar manner on the Poisson point process.
  • 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 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 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.

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