Seminars & Events for PACM/Applied Mathematics Colloquium

April 8, 2013
4:30pm - 6:00pm
Filtering in high dimension
PACM/Applied Mathematics Colloquium

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.

Speaker: Ramon van Handel, Princeton University, ORFE
Location:
Fine Hall 214
April 15, 2013
4:30pm - 5:30pm
Slow diffusion and transport in random media
PACM/Applied Mathematics Colloquium

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.

Speaker: Gerard Ben Arous, Courant Institute of Mathematics
Location:
Fine Hall 214
April 22, 2013
4:30pm - 6:00pm
Ozyesil: " 3D Motion Estimation by Convex Programming"
PACM/Applied Mathematics Colloquium

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.

Speaker: Caleb Bastian and Onur Ozyesil, PACM Graduate Students, Princeton University
Location:
Fine Hall 214
April 29, 2013
4:30pm - 5:30pm
A good lift: bipartite Ramanujan graphs of all degrees
PACM/Applied Mathematics Colloquium

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.

Speaker: Daniel Spielman, Yale University
Location:
Fine Hall 214