Calabi-Yau mirror symmetry: from categories to curve-counts

Tim Perutz
University of Texas at Austin
November 15, 2013
I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of the same conjecture which we expect to be much more amenable to proof; and, in ongoing work, (ii) that from HMS one can deduce (some of) the expected equalities between genus-zero Gromov-Witten invariants of a CY manifold and the Yukawa couplings of its mirror.

Science Talk for Families - The Smallest Particles

Robbert Dijkgraaf
November 16, 2013
One of the most amazing things we discovered in science is that everything is made of small particles. It's the properties of these molecules, atoms, nuclei, and elementary particles that allow us to answer ­simple questions like: why is grass green? Or, why is the sky blue? But how small are these particles? And how did we discover them? And does the search ever stop? To answer these questions we have to step into a world of wonder and magic.

Efficient reasoning in PAC semantics

Brendan Juba
Harvard University
November 18, 2013
Machine learning is often employed as one step in a larger application, serving to perform information extraction or data mining for example. The rules obtained by such learning are then used as inputs to a further analysis. As a consequence of the inputs to this analysis having been learned, however, its conclusions can only be theoretically guaranteed to satisfy the same standard as the inputs---that of "PAC Semantics" (Valiant, 2000).

Interacting Brownian motions in the Kadar-Parisi-Zhang universality class

Herbert Spohn
Technische Universitaet Muenchen; Member, School of Mathematics
November 18, 2013
A widely studied model from statistical physics consists of many (one-dimensional) Brownian motions interacting through a pair potential. The large scale behavior of this model has has been investigated by Varadhan, Yau, and others in the 90's. As a crucial property the model satisfies time-reversibility (alias detailed balance). Once this symmetry is broken, generically one crosses into the KPZ class. Two specific examples will be discussed.

Interactive Channel Capacity

Gillat Kol
Institute for Advanced Study; Member, School of Mathematics
November 19, 2013
In a profoundly influential 1948 paper, Claude Shannon defined the entropy function H, and showed that the capacity of a symmetric binary channel with noise rate (bit flip rate) eps is 1−H(eps). This means that one can reliably communicate n bits by sending roughly n/(1−H(eps)) bits over this channel. The extensive study of interactive communication protocols in the last decades gives rise to the related question of finding the capacity of a noisy channel when it is used interactively.

All-order asymptotics in beta ensembles in the multi-cut regime

Gaetan Borot
Max Planck Institute, Bonn
November 21, 2013
Based on joint work with A. Guionnet (MIT). The beta ensemble is a particular model consisting of N strongly correlated real random variables. For specific values of beta, it is be realized by the eigenvalues of a random hermitian matrix whose distribution is invariant by conjugation, and in this case the model is exactly solvable in terms of orthogonal polynomials, and provide solutions to the Toda chain equations.

Diffusion and superdiffusion of energy in one dimensional systems of oscillators

Stefano Olla
Dauphine Universite Paris
November 21, 2013
We consider a system of harmonic oscillators with stochastic perturbations of the dynamics that conserve energy and momentum. In the one dimensional unpinned case, under proper space-time rescaling, Wigner distribution of energy converges to the solution of a fractional heat equation (with power 3/4 for the laplacian). For pinned systems or in dimension 3 or higher, we prove normal diffusive behaviour. Similar results are also obtained for space-time energy correlations in equilibrium.