Past Seminars- Colloquium

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  • Alexander Kechris
    Thu Apr 17, 2014
    4:00 pm
    Recently there has been considerable activity in the study of the dynamics of these groups and this work has led to interesting interactions between logic, finite combinatorics, group theory (both in the topological and algebraic context), topological dynamics, ergodic theory and representation theory. In this lecture I will give a survey of some...
  • David Damanik
    Thu Apr 3, 2014
    4:00 pm
    A subset of the real line is called a Cantor set if it is compact, perfect, and nowhere dense. Cantor sets arise in many areas; in this talk we will discuss their relevance in the spectral theory of Schr\"odinger operators. We discuss several results showing that the spectrum of such an operator is a Cantor set, from the discovery of the...
  • Ciprian Manolescu
    Thu Mar 6, 2014
    4:00 pm
    The triangulation conjecture stated that any n-dimensional topological manifold is homeomorphic to a simplicial complex. It is true in dimensions at most 3, but false in dimension 4 by the work of Casson and Freedman. In this talk I will explain the proof that the conjecture is also false in higher dimensions. This result is based on previous...
  • Manjul Bhargava
    Thu Feb 27, 2014
    4:00 pm
    Given a random elliptic or hyperelliptic curve of genus g over Q, how many rational points do we expect the curve to have? Equivalently, how often do we expect a random polynomial of degree n to take a square value over the rational numbers?  In this talk, we give an overview of recent conjectures and theorems giving some answers and partial...
  • Hendrik Lenstra Jr.
    Tue Jan 7, 2014
    3:00 pm
    Given a polynomial map between two vector spaces over a field, how many values can it miss? The lecture will present a number of new results on this question. They were inspired by the work of Daqing Wan, and obtained jointly with Michiel Kosters (Leiden).
  • Jean-Pierre Bourguignon
    Thu Nov 7, 2013
    4:00 pm
    In the last century, Geometry underwent several substantial extensions and revisions based on the fundamental revolutions that it lived through in the XIXth century. The purpose of the lecture is to discuss several aspects of these transformations: the new concepts that emerged from these new points of view, the new perspectives that could be...
  • Eitan Tadmor
    Wed Jun 5, 2013
    4:00 pm
    We discuss self-organized dynamics of agent-based models with focus on a prototype model driven by non-symmetric self-alignment introduced in [1]. Unconditional consensus and flocking emerge when the self-alignment is driven by global interactions with a sufficiently slow decay rate.  In more realistic models, however, the interaction of...