# Seminars & Events for PACM/Applied Mathematics Colloquium

##### Filtering in high dimension

A problem that arises in many applications is to compute the conditional distributions of stochastic models given observed data. PLEASE CLICK ON COLLOQUIUM TITLE FOR COMPLETE ABSTRACT.

##### Slow diffusion and transport in random media

I will survey some fairly universal mechanisms which induce slow regimes for random walks. I will mainly give a few examples of dynamics in random media, where the complex geometry of the medium can induce interesting slow diffusion, in particular when a drift is added. The paradigm will be random walks on random trees or on percolation clusters. I will report on recent joint works with M.Cabezas, J. Cerny, A.Fribergh, A.Hammond, Y. Hu, N.Gantert, S. Olla, R. Royfman, V. Sidoravicius, and O.Zeitouni.

##### Ozyesil: " 3D Motion Estimation by Convex Programming"

3D structure recovery from a collection of 2D photos is a classical problem in computer vision that requires the estimation of the camera orientations and positions, i.e. the camera motion. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### A good lift: bipartite Ramanujan graphs of all degrees

We prove that there exist infinite families of bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph. We also construct infinite families of `irregular Ramanujan' graphs, whose eigenvalues are bounded by the spectral radius of their universal cover. In particular, we construct infinite families of (c,d)-biregular bipartite Ramanujan graphs for all c and d greater than 2. Our proof exploits a new technique for demonstrating the existence of useful combinatorial objects that we call the ``Method of Interlacing Polynomials''. The proofs are elementary, and the talk should be accessible to a broad audience. Joint work with Adam Marcus and Nikhil Srivastava.