Organizers: Patrick Brosnan, Sandra Cerrai, and Vadim Kaloshin
Wednesday @ 3:15pm, 2:45pm Tea in 3201
Math 3206
From time to time special colloquia are held on other days, sometimes as part of conferences.
Other special colloquia are the Aziz Lectures and Avron Douglis Memorial Lectures.

  • Aziz Lecture- TBA

    Speaker: Irene Fonseca (Carnegie Mellon University) -

    When: Wed, May 4, 2016 - 3:15pm
    Where: Math 3206
  • Polterovich (TBA)

    Speaker: Iosif Polterovich (Université de Montréal) -

    When: Wed, April 27, 2016 - 3:15pm
    Where: Math3206
  • Reserved for Dynamics Conference

    Speaker: Dynamics Conference (UMD) -

    When: Fri, April 15, 2016 - 3:15pm
    Where: Math 3206
  • Chen (TBA)

    Speaker: Xuewen Chen (University of Rochester) -

    When: Wed, April 13, 2016 - 3:15pm
    Where: 3206.0
  • Artificial Intelligence and data science from Eric Horvitz (Microsoft) and DJ Patil (White House)

    When: Fri, April 8, 2016 - 9:00am
    Where: Time and Place to be determined
  • Lubetzky (TBA)

    Speaker: Eyal Lubetzky (NYU) -

    When: Wed, April 6, 2016 - 3:15pm
    Where: Math 3206
  • Bismut (TBA)

    Speaker: Jean-Michel Bismut (Université Paris-Sud) -

    When: Wed, March 9, 2016 - 3:05pm
    Where: 3201.0
  • Kontorovich (TBA)

    Speaker: Alex Kontorovich (Rutgers University) -

    When: Fri, March 4, 2016 - 3:15pm
    Where: Math 3206
  • Discussion with EPSL Head Librarian

    Speaker: Nevenka Zdravkovska (UMCP Libraries) -

    When: Wed, March 2, 2016 - 3:15pm
    Where: Math 3206
  • Parimala (TBA)

    Speaker: R. Parimala (Emory ) -

    When: Fri, February 26, 2016 - 3:15pm
    Where: Math 3206
  • Global controllability to trajectories for the viscous Burgers equation

    Speaker: Armen Shirikyan (Université de Cergy-Pontoise ) -

    When: Wed, February 24, 2016 - 3:15pm
    Where: 3206.0

    View Abstract

    Abstract: We study the problem of global controllability by an external force for the viscous Burgers equation on a bounded interval. Assuming that the force is localised in space, we prove that any non-stationary trajectory can be exponentially stabilised. We next discuss various consequences of this result, including global exact controllability to trajectories and approximate controllability by a localised low-dimensional control.
  • Singularity formation in nonlinear PDE’s: a qualitative approach

    Speaker: Pierre Raphael (U. Nice Sophia Antipolis) -

    When: Wed, February 17, 2016 - 11:00am
    Where: Math 3206

    View Abstract

    Abstract: The qualitative study of nonlinear partial differential equations has made spectacular progress in the past 30 years. Various deep nonlinear phenomenons have now been exhibited, at least on some canonical simplified models extracted from physics. I shall report in this talk onto one specific phenomenon: singularity formation, and more generally energy concentration. I will illustrate on some canonical models (like the seminlinear heat or Schrodinger equation) how one can construct and completely understand some scenarios of energy concentration, and how a complete classification of such blow up dynamics can sometimes be obtained. At the heart of the analysis lies a fundamental nonlinear object: the solitary wave.
  • Equidistribution of Frobenius eigenvalues

    Speaker: Kiran Kedlaya (UCSD) -

    When: Fri, February 12, 2016 - 3:15pm
    Where: 3206.0

    View Abstract

    Abstract: Consider a system of polynomial equations with integer coefficients. For
    each prime number p, one can count the solutions of these equtaions in
    the integers modulo p; while the structure of these counts is a rather
    deep topic in number theory, one can pose statistical questions about
    these counts for which the answers are expected to be somewhat simpler
    (although still deep). We discuss several variations on this theme,
    including the Chebotarev density theorem, the Sato-Tate conjecture for
    elliptic curves, a general but imprecise conjecture of Serre, and a
    precise form of Serre's conjecture for genus 2 curves due to

  • p-adic uniformization of Shimura curves

    Speaker: Michael Rapoport (Universitaet Bonn ) -

    When: Wed, February 10, 2016 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Shimura curves are algebraic curves that arise through complex
    uniformization by an arithmetic group acting on the complex half
    plane. Forty years ago, Cherednik observed that under suitable
    assumptions, these curves can also be uniformized by the Drinfeld
    p-adic half plane. Now we are close to a reasonable proof (of a
    variant) of this statement.
    I will report on joint work with S. Kudla and Th. Zink, and related
    work of P. Scholze.
  • ENIGMA: Harnessing mathematics in cryptology

    Speaker: Roman Sznajder (Bowie State University) -

    When: Fri, January 29, 2016 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: ENIGMA was a German ciphering machine developed soon after WWI for commercial use. Shortly after, it was acquired by the German army and used for encrypting and decrypting military messages and orders. We discuss the circumstances that led to the initial breaking of the Enigma code in 1932 by three young cryptologists: Rejewski, Różycki, and Zygalski from the Polish Cipher Office. This was the first time when mathematics was systematically used in cryptography. Specifically, there were applications of permutation groups used to reconstruct the wiring of military Enigma and then to recover the daily keys and keys for individual messages. In the summer of 1939, when the outbreak of WWII was imminent, the Polish Cipher Office provided Allies with two copies of the Enigma machine and daily keys. Aided by these materials, the British immediately began working on breaking Enigma messages. Their office in Bletchley Park had access to human, engineering, and technological resources on an industrial scale. The ability to read encrypted messages used by the German army—enabled by the breaking of the Enigma code—contributed to the shortening of WWII and, according to some estimates, spared several million lives. With the British WWII archives sealed and Poland behind the Iron Curtain, the British Secret Service suppressed the knowledge about the role of Polish intelligence in breaking the Enigma code for about thirty years. The heroic effort of three Polish cryptologists was virtually unknown to the world until the 1973 publication of a book by the French general Gustave Bertrand. In this presentation, we will shed some light on mathematical methods, the events and people involved in the successful effort to break the Enigma code.
  • A drunk walk in a drunk world

    Speaker: Ivan Corwin (Columbia University, Clay Mathematics Institute) -

    When: Wed, December 9, 2015 - 3:15pm
    Where: Math3206

    View Abstract

    Abstract: In a simple symmetric random walk on Z a particle jumps left or right with 50% chance independently at each time and space location. What if the jump probabilities are taken to be random themselves (e.g. uniformly distributed between 0% and 100%). In this talk we will describe the effect of this random environment on a random walk, in particular focusing on a new connection to the Kardar-Parisi-Zhang universality class and to the theory of quantum integrable systems. No prior knowledge or background will be expected.
  • Tensor Sparsity - a Regularity Notion for High Dimensional PDEs [Aziz Lecture]

    Speaker: Wolfgang Dahmen (Aachen University, Germany) -

    When: Wed, November 18, 2015 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: The numerical solution of PDEs in a spatially high-dimensional regime (such as the electronic Schrodinger or Fokker-Planck
    equations) is severely hampered by the "curse of dimensionality":
    the computational cost required for achieving a desired target accuracy increases exponentially with respect to the spatial dimension.

    We explore a possible remedy by exploiting a typically hidden sparsity of the solution to such problems with respect to a problem dependent basis or dictionary. Here sparsity means that relatively few terms from such a dictionary suffice to realize a given target accuracy. Specifically, sparsity with respect to dictionaries comprised of separable functions -- rank-one tensors
    -- would significantly mitigate the curse of dimensionality. The main result establishes such tensor-sparsity for elliptic problems over product domains when the data are tensor-sparse, which can be viewed as a structural regularity theorem.

  • Geometry of ODE's with a small parameter

    Speaker: Dima Arinkin (University of Wisconsin) -

    When: Wed, November 11, 2015 - 3:15pm
    Where: 3206.0

    View Abstract

    Abstract: I will look at very classical objects (linear ordinary differential equations) and study them from the view-point of algebraic geometry. The starting point is some simple results about differential operators of the form h(d/dx)+A(x), where h is small. The results lead to a non-trivial and beautiful picture for the parameter space of such equations, which may be interpreted geometrically as the moduli space of bundles with connections on a Riemann surface.
  • John Horvath remembrance event

    Speaker: Hold Date () -

    When: Wed, November 4, 2015 - 3:15pm
    Where: Math 3206
  • No Colloquium

    Speaker: No Colloquium () -

    When: Fri, October 30, 2015 - 3:15pm
    Where: Math 3206
  • No Seminar

    Speaker: No Seminar () -

    When: Wed, October 28, 2015 - 3:15pm
    Where: Math 3206
  • No Seminar

    Speaker: No Seminar () -

    When: Wed, October 21, 2015 - 3:15pm
    Where: Math 3206
  • Milnor-Witt K-Theory

    Speaker: Stefan Gille (Alberta) -

    When: Wed, October 14, 2015 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Milnor-Witt K-theory arises in the Morel-Voevodsky homotopy theory over a field and plays a role in the classification of vector bundles over smooth schemes. Morel in collaboration with Hopkins discovered a nice presentation of these groups, which has been recently generalized by Changlong Zhong, Stephen Scully and myself to semilocal rings which contain an infinite field. In my talk I will discuss this result and also present some applications of these groups.
  • Colloquium supeseded by Math Department Welcome

    Speaker: Math Department Welcome () -

    When: Fri, September 25, 2015 - 3:15pm
    Where: Math 3206
  • Galileo's New Mathematics

    Speaker: Mark A. Peterson (Mount Holyoke College) -

    When: Wed, September 16, 2015 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Galileo isn't really remembered for his mathematics.
    There is nothing called "Galileo's Theorem," for instance.
    But Galileo did make a fundamental contribution to mathematics,
    arguably more important than any new theorem, namely a new (or re-discovered)
    conception of what mathematics could mean. In the decades before
    Galileo, higher mathematics was an essentially static and obscure
    corner of philosophy, barely connected to physical reality.
    After Galileo, mathematics became the scaffolding
    of physics, and (apparently as a consequence) subject to rapid development.
    This revolution in Galileo's thought, and in the philosophy of
    mathematics more generally, had to come from outside mathematics:
    in Galileo's case it had its roots in literature, the arts, and quite
    possibly the theology of the High Middle Ages.
  • Hodge Theory on Matroids

    Speaker: Eric Katz (Univerisity of Waterloo) -

    When: Wed, September 9, 2015 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: The chromatic polynomial of a graph counts its proper colourings. This polynomial's coefficients were conjectured to form a unimodal sequence by Read in 1968. This conjecture was extended by Rota in his 1970 address to assert the log-concavity of the characteristic polynomial of matroids which are the common generalizations of graphs and linear subspaces. We discuss the resolution of this conjecture which is joint work with Karim Adiprasito and June Huh. The solution draws on ideas from the theory of algebraic varieties, specifically Hodge theory, showing how a question about graph theory leads to a solution involving Grothendieck's standard conjectures.