Previous Conferences & Workshops

The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. In this talk, based on joint work with Tom Parker, I describe the proof...

To any bounded family of \(\mathbb F_\ell\)-linear representations of the etale fundamental of a curve \(X\) one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves with level \(\ell\)...

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...

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...

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) \(\mathrm{eps}\) is \(1-H(\mathrm{eps})\). This means that one can...

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...

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...