SegalBargmann Transform in Noncommutative Probability 

Natasha Blitvic (Indiana)
I will give an introduction to noncommutative probability, a vibrant area at the interface of (classical) probability, operator algebras, combinatorics, and mathematical physics. We will discuss some ways in which the noncommutative theory parallels and contrasts with the classical theory. The motivation will be the recent joint work with T. Kemp on the extension of the SegalBargmann analysis to an interesting twoparameter family of noncommutative probability spaces. top of page

Multilevel Dyson Brownian Motion and its edge limits 

Vadim Gorin (MIT)
The GUE TracyWidom distribution is known to govern the largetime asymptotics for a variety of interacting particle systems on one side, and the asymptotic behavior for largest eigenvalues of random Hermitian matrices on the other side. In my talk I will explain some reasons for this connection between two seemingly unrelated classes of stochastic systems, and how this relation can be extended to general beta random matrices. A multilevel extension of the Dyson Brownian Motion will be the central object in the discussion. (Based on joint papers with Misha Shkolnikov). top of page

Stochastic PDEs and Turbulence


Nathan GlattHoltz (Virginia Tech)
I will survey some recent results concerning the ergodic theory of nonlinear stochastic PDEs and describe how these results have bearing on various statistical theories of turbulent fluid flow. top of page

Lengths of Monotone Subsequences in a Mallows Permutation 

Naya Bhatnagar (U Delaware)
The longest increasing subsequence (LIS) of a uniformly random permutation is a well studied problem. VershikKerov and LoganShepp first showed that asymptotically the typical length of the LIS is 2sqrt(n). This line of research culminated in the work of BaikDeiftJohansson who related this length to the TracyWidom distribution.
We study the length of the LIS and LDS of random permutations drawn from the Mallows measure, introduced by Mallows in connection with ranking problems in statistics. Under this measure, the probability of a permutation p in S_n is proportional to q^{Inv(p)} where q is a real parameter and Inv(p) is the number of inversions in p. We determine the typical order of magnitude of the LIS and LDS, large deviation bounds for these lengths and a law of large numbers for the LIS for various regimes of the parameter q.
This is joint work with Ron Peled. top of page



