Colloquium

  • 2017 Sep 14

    Colloquium: Kate Juschenko (Northwestern University) - "Cycling amenable groups and soficity"

    2:30pm to 3:30pm

    Location: 

    IIAS hall, Hebrew University Jerusalem
    I will give introduction to sofic groups and discuss a possible strategy towards finding a non-sofic group. I will show that if the Higman group were sofic, there would be a map from Z/pZ to itself, locally like an exponential map, satisfying a rather strong recurrence property. The approach to (non)-soficity is based on the study of sofic representations of amenable subgroups of a sofic group. This is joint work with Harald Helfgott.
  • 2017 Jun 22

    Colloquium: Zohovitzki prize lecture - Ariel Rapaport, "Self-affine measures with equal Hausdorff and Lyapunov dimensions"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    A measure on the plane is called self-affine if it is stationary with respect to a finitely supported measure on the affine group of R^2. Under certain randomization, it is known that the Hausdorff dimension of these measures is almost surely equal to the Lyapunov dimension, which is a quantity defined in terms of the linear parts of the affine maps. I will present a result which provides conditions for equality between these two dimensions, and connects the theory of random matrix products with the dimension of self-affine measures.
  • 2017 Jun 15

    Colloquium: Alexander Logunov (Tel Aviv), "0,01% Improvement of the Liouville property for discrete harmonic functions on Z^2"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Let u be a harmonic function on the plane.
    The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant.
    It appears that if u is a harmonic function on a lattice Z^2, and |u| < 1 on 99,99% of Z^2,
    then u is a constant function.
     
    Based on a joint work(in progress) with L.Buhovsky, Eu.Malinnikova and M.Sodin.
     
  • 2017 Jun 08

    Colloquium:  Vadim Kaloshin (Maryland) - "Birkhoff Conjecture for convex planar billiards and deformational spectral rigidity of planar domains"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    G.D.Birkhoff introduced a mathematical billiard inside of a convex domain as the motion
    of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says
    that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the
    boundary is foliated by smooth closed curves and each billiard orbit near the boundary
    is tangent to one and only one such curve (in this particular case, a confocal ellipse).
    A famous conjecture by Birkhoff claims that ellipses are the only domains with this
  • 2017 Jun 08

    Wolf Prize Lecture - Rick Schoen (Stanford): The geometry of eigenvalue extremal problems

    11:00am to 12:00pm

    Location: 

    Levin building, lecture hall 8
    Title: “The geometry of eigenvalue extremal problems”
    Abstract: When we choose a metric on a manifold we determine the spectrum of
    the Laplace operator. Thus an eigenvalue may be considered as a functional
    on the space of metrics. For example the first eigenvalue would be the fundamental
    vibrational frequency. In some cases the normalized eigenvalues are bounded
    independent of the metric. In such cases it makes sense to attempt to find
    critical points in the space of metrics. In this talk we will survey two cases in
  • 2017 May 18

    Colloquium: Alex Eskin (Chicago) Dvoretzky Lecure Series, "Polygonal Billiards and Dynamics on Moduli Spaces."

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Billiards in polygons can exhibit some bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry (and in particular Hodge theory), Teichmuller theory and ergodic theory on homogeneous spaces. I will attempt to give a gentle introduction to the subject. A large part of this talk will be accessible to undergraduates.
  • 2017 May 04

    Colloquium: Jozsef Solymozi (UBC) Erdos Lecture Series, "The sum-product problem"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    The incompatibility of multiplicative and additive structures in various fields and rings is an important phenomena. In this talk I will talk about a special case of it. Let us consider a finite subset of integers, A. The sum set of A is the set of pairwise sums of elements of A and the product set is the set of pairwise products. Erdős and Szemeredi conjectured that either the sum set or the product set should be large, almost quadratic in size of A. The conjecture is still open. Similar questions can be asked over any ring or field.
  • 2017 Apr 27

    Colloquium: Gal Binyamini (Weizmann), " Differential equations and algebraic points on transcendental varieties"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    The problem of bounding the number of rational or algebraic points of a given height in a transcendental set has a long history. In 2006 Pila and Wilkie made fundamental progress in this area by establishing a sub-polynomial asymptotic estimate for a very wide class of transcendental sets. This result plays a key role in Pila-Zannier's proof of the Manin-Mumford conjecture, Pila's proof of the Andre-Oort conjecture for modular curves, Masser-Zannier's work on torsion anomalous points in elliptic families, and many more recent developments.
  • 2017 Apr 20

    Colloquium - Avraham (Rami) Aizenbud (Weizmann), "Representation count as a Meeting Point for Analysis, Arithmetic, Geometry and Algebra"

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Consider the following questions:
    1. How does the volume of the set f(x_1,...,x_d) < epsilon behaves when epsilon goes to 0?
    2. How does the number of solutions of the equation f(x_1,...,x_d) = 0 (mod n) behaves when n goes to infinity.
    I will present these and other questions which looks as if they are taken from different areas of mathematics. I'll explain the relation between those questions. Then I'll explain how this relation is used in order to show the following theorem answering a question of Larsen and Lubotzky:

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