Inaugural Rollo Davidson Lecture

    Persi Diaconis (Harvard)
    The mathematics of making a mess
    Wednesday 8th May 1996, 17:00-18:00
    Room 9, Mill Lane Lecture Rooms
    It takes about seven ordinary riffle shuffles to mix 52 cards. The argument involves the descent theory of the symmetric group and yields a Hodge decompsition for Hochschild homology. As well as some new card tricks…

Second Rollo Davidson Lecture

    Wendelin Werner (Universite Paris-Sud)
    Random planar curves and conformal invariance
    Tuesday 10 July 2001, 18:-19:00
    Wolfson Hall, Churchill College, Cambridge
    Understanding the behaviour of certain natural very long random curves in the plane is a seemingly simple question that has turned out to raise deep questions, some of which remain unsolved. For instance, theoretical physicists have predicted (and this is still an open problem) that the number a(N) of self-avoiding curves of length N on the square lattice Z × Z grows asymptotically like CN N11/32 for some constant C. More generally, theoretical physicists (Nienhuis, Cardy, Duplantier, Saleur etc.) have made predictions concerning the existence and values of critical exponents for various two-dimensional systems in statistical physics (such as self-avoiding walks, critical percolation, intersections of simple random walk) using considerations related to several branches of mathematics (probability theory, complex variables, representation theory of infinite-dimensional Lie algebras). We give a general introduction to the subject and briefly present some recent mathematical progress, including work of Kenyon, Werner, Smirnov, Lawler, and Schramm.

Third Rollo Davidson Lecture

    Professor Stanislav Smirnov (University of Geneva)
    Discrete complex analysis and probability
    Wednesday, 05 May, 2010 at 5.00pm
    Wolfson Lecture Room (AL.06) Centre for Mathematical Sciences.
    Most 2D lattice models (percolation, Ising, self-avoiding polymers) are conjectured to have conformally invariant scaling limits at critical temperatures, which were used by physicists in deriving many of their properties. Proving these conjectures requires finding "discrete conformal invariants" associated with the models.
    We will discuss the concept of a "discrete complex analysis" and how it is relevant in probabilistic structures.

Fourth Rollo Davidson Lecture

    Yuval Peres (Microsoft Research, Redmond)
    Random walk on the random graph
    will discuss the behavior of the random walk on two random graph models: on one hand the random regular graph with constant degree, and on the other hand the giant component of the supercritical Erdos-Renyi random graph with constant average degree. In the former case it is known that the walk mixes in logarithmic time and exhibits the cutoff phenomenon. In the latter case, while starting from the worst trap delays mixing and precludes cutoff, it turns out that starting from a fixed vertex induces the rapid mixing behavior of the regular case. (Joint work with Nathanael Berestycki, Eyal Lubetzky and Allan Sly.)