Colloquium

  • 2019 Apr 11

    Colloquium: Ohad Feldheim - Lattice models of magnetism: from magnets to antiferromagnets

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem

    Abstract:
    The Ising model, and its generalisation, the Potts model, are two classical graph-colouring models for magnetism and antiferromagnetism. Albeit their simple formulation, these models were instrumental in explaining many real-world magnetic phenomena and have found various applications in physics, biology and computer science. While our understanding of these models as modeling magnets has been constantly improving since the early twentieth century, little progress was made in treatment of Potts antiferromagnets.
  • 2019 Apr 04

    Colloquium: Uri Shapira (Technion) - Dynamics on hybrid homogeneous spaces

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Abstract: I will discuss a collection of results about lattices and their subgroups in Euclidean space which are obtained using dynamics on homogeneous spaces. The ergodic theory of group actions on spaces obtained by quotienning a Lie group by a lattice (spaces of lattice-type) or on projective spaces are extensively studied and display distinct dynamical phenomena. Motivated by classical questions in Diophantine approximation we are led to study the ergodic theory of group actions on hybrid homogeneous spaces which are half projective and half of lattice type.
  • 2019 Mar 14

    Colloquium: Alexander Bors (University of Western Australia) - Finite groups with a large automorphism orbit

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Abstract: If X is an object such that the notion of an automorphism of X is defined (e.g.,
    an algebraic structure, a graph, a topological space, etc.), then one can define an
    equivalence relation ∼ on X via x ∼ y if and only if α(x) = y for some automorphism
    α of X. The equivalence classes of ∼ are called the automorphism orbits of X.
    Say that X is highly symmetric if and only if all elements of X lie in the same
    automorphism orbit. Finite highly symmetric objects are studied across various
  • 2019 Jan 17

    Colloquium: Lior Bary-Soroker (TAU) - Virtually all polynomials are irreducible

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    It has been known for almost a hundred years that most polynomials with integral coefficients are irreducible and have a big Galois group. For a few dozen years, people have been interested in whether the same holds when one considers sparse families of polynomials—notably, polynomials with plus-minus 1 coefficients. In particular, “some guy on the street” conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity (a much earlier conjecture of Odlyzko-Poonen is about the 0-1 coefficients model).
  • 2019 Jan 10

    Joram Seminar: Larry Guth (MIT) - Introduction to decoupling

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Decoupling is a recent development in Fourier analysis. In the late 90s, Tom Wolff proposed a decoupling conjecture and made the first progress on it. The full conjecture had seemed well out of reach until a breakthrough by Jean Bourgain and Ciprian Demeter about five years ago.
    Decoupling has applications to problems in PDE and also to analytic number theory. One application involves exponential sums, sums of the form
    $$\sum_j e^{2 pi i \omega_j x}.$$
  • 2019 Jan 03

    Colloquium: Nati Linial (HUJI) - Graph metrics

    2:30pm to 3:30pm

    A finite graph is automatically also a metric space, but is there any interesting geometry to speak of? In this lecture I will try to convey the idea that indeed there is very interesting geometry to explore here. I will say something on the local side of this as well as on the global aspects. The k-local profile of a big graph G is the following distribution. You sample uniformly at random k vertices in G and observe the subgraph that they span. Question - which distributions can occur? We know some of the answer but by and large it is very open.

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