2005-2006 seminars

We analyze volume-preserving actions of product groups on Riemannian manifolds. Under a natural spectral irreducibility assumption, we prove the following dichotomy: Either the action is measurably isometric, in which case there are at most two...

I will survey a number of settings withing theoretical computer sceince in which certain computations are abstracted by "black boxes", namely devices for which we can observe the input-output behavior, but not the actual "guts" of the computation. I...

In this talk, we will sketch the theory of simultaneous optimization for concave profit functions, and point out connections to fairness. More precisely, suppose we would like to simultaneously approximate all symmetric utility functions over a...

We introduce a new algorithm and a new analysis technique that is applicable to a variety of online optimization scenarios, including regret minimization for Lipschitz regret functions, universal portfolio management, online convex optimization and...

In previous work we showed that arithmetic hyperbolic 2-manifolds that are isospectral are commensurable. In this talk we discuss the proof of the generalization to dimension 3. We had previously shown that if arithmetic hyperbolic 3-manifolds are...

We consider periodic orbits of multiparameter diagonalizable actions. A simple example of such an action is the action generated by the maps x -> 2x mod 1 and x -> 3x mod 1 on R/Z. There are strong parallels between the study of these orbits and...

We propose a new approach to designing a strongly polynomial algorithm for linear programming. We show that linear programming on any polytope can be reduced to linear programming on an arrangement polytope. The graphs of arrangement polytopes have...