Past Seminars

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  • Mathematical Physics
    Absence of point spectrum for the self-dual Extended Harper's Model
    Christoph Marx
    Thu May 9, 2013
    2:00 pm
    An interesting feature of extended Harper's model (EHM), a generalization of the almost Mathieu operator popularized by DJ Thouless, is the appearance of a large regime of coupling parameters invariant under Aubry duality (``self-dual regime''). In this regime, extensive numerical analysis in physics literature conjecture a ``strange...
  • Cryptography
    Candidate Multilinear Maps from Ideal Lattices
    Sanjam Garg
    Tue May 7, 2013
    3:00 pm
    We describe plausible lattice-based constructions with properties that approximate the sought-after multilinear maps in hard-discrete-logarithm groups, and show an example application of such multilinear maps that can be realized using our approximation. The security of our constructions relies on seemingly hard problems in ideal lattices, which...
  • Mathematical Physics
    Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles
    Silvius Klein
    Tue May 7, 2013
    3:00 pm
    Consider an m-dimensional analytic cocycle with underlying dynamics given by an irrational translation on the circle. Assuming that the d-dimensional upper left corner of the cocycle is typically large enough, we prove that the d largest Lyapunov exponents associated with this cocycle are bounded away from zero. The result is...
  • Number Theory
    Explicit zeta functions for a class of hyperelliptic curves
    Shuhong Gao
    Tue May 7, 2013
    2:00 pm
    In this talk, we show how to explicitly determine the zeta functions of hyperelliptic curves of the form $y^2 = x^p-ax-b$ defined over a finite field $GF(p^s}$ where $p$ is a prime. Joint work with Hui Xue and Lin You.
  • Dynamical Systems
    (Pseudo)-groups acting on the circle: towards a characterization theorem
    Victor Klepstyn
    Tue May 7, 2013
    1:00 pm
    Take a finitely-generated group of (analytic) circle diffeomorphisms. Since the times of Poincaré we know that any such action admits either a finite orbit, or a Cantor minimal set, or the action is minimal on all the circle. But what else can be said on such a group? In this direction, there are well-known questions due to Sullivan, Ghys...
  • Lee Yang Circle Theorem and the Reimann Hypothesis
    Chuck Newman
    Tue May 7, 2013
    11:00 am
    In this talk we discuss a connection between statistical mechanics and the Riemann hypothesis in number theory.
  • Applied and Computational Mathematics
    Spare Approximation via Penalty Decomposition and Iterative Hard Thresholding...
    Zhaosong Lu
    Mon May 6, 2013
    4:00 pm
    In the first part, we discuss penalty decomposition (PD) methods for solving a more general class of $l_0$ minimization in which a sequence of penalty subproblems are solved by a block coordinate descent (BCD) method. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the PD methods satisfies...