Loops in hydrodynamic turbulence

Katepalli Sreenivasan
New York University; Member, School of Mathematics
April 17, 2019
An important question in hydrodynamic turbulence concerns the scaling proprties in the inertial range. Many years of experimental and computational work suggests---some would say, convincingly shows---that anomalous scaling prevails. If so, this rules out the standard paradigm proposed by Kolmogorov. The situation is not so obvious if one considers circulation around loops as the scaling objects instead of the traditional velocity increments.

On the possibility of an instance-based complexity theory.

Boaz Barak
Harvard University
April 15, 2019
Worst-case analysis of algorithms has been the central method of theoretical computer science for the last 60 years, leading to great discoveries in algorithm design and a beautiful theory of computational hardness. However, worst-case analysis can be sometimes too rigid, and lead to an discrepancy between the "real world" complexity of a problem and its theoretical analysis, as well as fail to shed light on theoretically fascinating questions arising in connections with statistical physics, machine learning, and other areas.

Etale and crystalline companions

Kiran Kedlaya
University of California, San Diego; Visiting Professor, School of Mathematics
April 15, 2019

Deligne's "Weil II" paper includes a far-reaching conjecture to the
effect that for a smooth variety on a finite field of characteristic p,
for any prime l distinct from p, l-adic representations of the etale
fundamental group do not occur in isolation: they always exist in
compatible families that vary across l, including a somewhat more
mysterious counterpart for l=p (the "petit camarade cristallin"). We
explain in more detail what this all means, indicate some key

Space-time correlations at equilibrium

Laure Saint-Raymond
University Paris VI Pierre et Marie Curie and Ecole Normale Supérieure
April 9, 2019
Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales.

    How combinatorial techniques can help to analyze this departure from chaos?

    Bifurcating conformal metrics with constant Q-curvature

    Renato Bettiol
    City University of New York
    April 9, 2019

    The problem of finding metrics with constant Q-curvature in a prescribed conformal class is an important fourth-order cousin of the Yamabe problem. In this talk, I will explain how certain variational bifurcation techniques used to prove non-uniqueness of solutions to the Yamabe problem also yield non-uniqueness results for the constant Q-curvature problem. However, special emphasis will be given to the differences between multiplicity phenomena in these two variational problems. This is based on joint work with P. Piccione and Y. Sire.