Past Events

This is the story of my odyssey—between China, Hong Kong, and the United States. I have traveled the world in my pursuit of geometry—a field that is crucial to our attempts to map out the universe on both the largest and smallest scales. Conjectures have been made during these excursions, “open…

Credit risk models largely bifurcate into two classes — the structural models and the reduced form models. Attempts have been made to reconcile the two approaches by adjusting filtrations to restrict information (Cetin, Jarrow, Protter, and Yldrm, Jarrow and Protter, and Giesecke) but they are…

At the end of the 1990s it was discovered by Jordan/Kinderlehrer/Otto that the diffusion equation is a gradient flow in the space of probability measures, where the driving functional is the Boltzmann-Shannon entropy, and the dissipation mechanism is given by the 2-Wasserstein metric from…

I will present effective methods to compute equivariant harmonic maps, both discrete and smooth. The main setting will be equivariant maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is…

I’ll discuss a spin-off from joint work with local physicists: Lenny Susskind and Adam Brown. We find an upper bound on the volume of balls in a Riemannian manifold X somewhat stronger (i.e. smaller) than that obtained by comparing to the hyperbolic space of equal dimension and Ricci quadratic…

I will discuss applications of tropical geometry to the cohomology of moduli spaces of curves, with and without marked points. Based on joint work with Melody Chan, Carel Faber, and Soren Galatius.

Logic adds an additional dimension to the study of random combinatorial structures, seeking results for all properties expressible in a given logical structure. In the classic Galton-Watson tree (each node having Poisson mean c children) the property of being infinite is given by a tree…

Paul selects n vectors in n-space, all coordinates one or minus one. Carole is a balancer, assigning signs to each vector yielding a signed vector sum P. The value V, which Carole attempts to minimize, is the maximal absolute value of the coordinates of P.

We consider four variants of…