Colloquium

  • 2018 Dec 27

    Colloquium: Alexander Yom Din (Caltech) - From analysis to algebra to geometry - an example in representation theory of real groups

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation.
  • 2018 Dec 20

    Colloquium: Assaf Rinot (Bar-Ilan) - Hindman’s theorem and uncountable Abelian groups

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    In the early 1970’s, Hindman proved a beautiful theorem in
    additive Ramsey theory asserting that for any partition of the set of
    natural numbers into finitely many cells, there exists some infinite set
    such that all of its finite sums belong to a single cell.
    In this talk, we shall address generalizations of this statement to the
    realm of the uncountable. Among other things, we shall present a
    negative partition relation for the real line which simultaneously
    generalizes a recent theorem of Hindman, Leader and Strauss, and a
  • 2018 Dec 13

    Erdos Lectures: Igor Pak (UCLA) - Counting integer points in polytopes

    Lecturer: 

    Igor Pak (UCLA)
    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Given a convex polytope P, what is the number of integer points in P? This problem is of great interest in combinatorics and discrete geometry, with many important applications ranging from integer programming to statistics. From a computational point of view it is hopeless in any dimensions, as the knapsack problem is a special case. Perhaps surprisingly, in bounded dimension the problem becomes tractable. How far can one go? Can one count points in projections of P, finite intersections of such projections, etc?
  • 2018 Dec 06

    Colloquium: Naomi Feldheim (Bar-Ilan) - A spectral perspective on stationary signals

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    A ``random stationary signal'', more formally known as a Gaussian stationary function, is a random function f:R-->R whose distribution is invariant under real shifts (hence stationary), and whose evaluation at any finite number of points is a centered Gaussian random vector (hence Gaussian).
    The mathematical study of these random functions goes back at least 75 years, with pioneering works by Kac, Rice and Wiener, who were motivated both by applications in engineering and
    by analytic questions about ``typical'' behavior in certain classes of functions.
  • 2018 Nov 29

    Colloquium: Chaya Keller (Technion) - Improved lower and upper bounds on the Hadwiger-Debrunner numbers

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    A family of sets F is said to satisfy the (p,q)-property if among any p sets in F, some q have a non-empty intersection. Hadwiger and Debrunner (1957) conjectured that for any p > q > d there exists a constant c = c_d(p,q), such that any family of compact convex sets in R^d that satisfies the (p,q)-property, can be pierced by at most c points. Helly's Theorem is equivalent to the fact that c_d(p,p)=1 (p > d).
  • 2018 Nov 22

    Colloquium: Spencer Unger (HUJI) - A constructive solution to Tarski's circle squaring problem

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    In 1925, Tarski asked whether a disk in R^2 can be partitioned into finitely many pieces which can be rearranged by isometries to form a square of the same area. The restriction of having a disk and a square with the same area is necessary. In 1990, Laczkovich gave a positive answer to the problem using the axiom of choice. We give a completely explicit (Borel) way to break the circle and the square into congruent pieces. This answers a question of Wagon. Our proof has three main components. The first is work of Laczkovich in Diophantine approximation.
  • 2018 Nov 15

    Colloquium: Ari Shnidman (Boston College) - Rational points on elliptic curves in twist families

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    The rational solutions on an elliptic curve form a finitely generated abelian group, but the maximum number of generators needed is not known. Goldfeld conjectured that if one also fixes the j-invariant (i.e. the complex structure), then 50% of such curves should require 1 generator and 50% should have only the trivial solution. Smith has recently made substantial progress towards this conjecture in the special case of elliptic curves in Legendre form. I'll discuss recent work with Lemke Oliver, which bounds the average number of generators for general j-invariants.
  • 2018 Nov 08

    Colloquium: Nathan Keller (Bar Ilan) - The junta method for hypergraphs and the Erdos-Chvatal simplex conjecture

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Numerous problems in extremal hypergraph theory ask to determine the maximal size of a k-uniform hypergraph on n vertices that does not contain an 'enlarged' copy H^+ of a fixed hypergraph H. These include well-known problems such as the Erdos-Sos 'forbidding one intersection' problem and the Frankl-Furedi 'special simplex' problem.
  • 2018 Nov 01

    Colloquium: Natan Rubin (BGU) - Crossing Lemmas, touching Jordan curves, and finding large cliques

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    It is a major challenge in Combinatorial Geometry to understand the intersection structure of the edges in a geometric or topological graph, in the Euclidean plane. One of the few "tight" results in this direction is the the Crossing Lemma (due to Ajtai, Chvatal, Newborn, and Szemeredi 1982, and independently Leighton 1983). It provides a relation between the number of edges in the graph and the number of crossings amongst these edges. This line of work led to several Ramsey-type questions of geometric nature.
  • 2018 Oct 25

    Colloquium: Karim Adiprasito (HUJI) - Combinatorics, topology and the standard conjectures beyond positivity

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2 or higher can it have? How dense can they be?
    This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar).
    All notions used will be explained in the talk (I will make an effort to be very elementary)

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