Fall 2013
Monday 4.15  5.15 pm
Room E17139
Schedule

September 9
Omer Tamuz (Microsoft Research / MIT)
Invariant random subgroups, the Poisson boundary and group action rigidity
Abstract: An Invariant Random Subgroup (IRS) is a subgroupvalued random variable that is invariant to conjugation  a probabilistic generalization of a normal subgroup. In this talk we will explain how, using IRSs, and using other probabilistic constructions such as random walks on groups and their Poisson boundaries, one can study the algebraic properties of a group and the properties of the probability spaces on which it acts.
We will discuss some old results and some new ones. This is based off of joint work with Yair Hartman.

September 16
Naomi Feldheim (Tel Aviv University)
New results on zeroes of stationary Gaussian functions
Abstract: We consider (complex) Gaussian analytic functions on a horizontal strip, whose distribution is invariant with respect to horizontal shifts (i.e., "stationary"). Let N(T) be the number of zeroes in [0,T] x [a,b]. First, we present an extension of a result by Wiener, concerning the existence and characterization of the limit N(T)/T as T approaches infinity. Secondly, we characterize the growth of the variance of N(T). For the last part, we consider real stationary Gaussian functions on the real axis and discuss the "gap probability" (i.e., the probability that the function has no zeroes in [0,T]). This part is a joint work with Ohad Feldheim.

September 2022
Special event at Boston University!

September 23
Scott Sheffield (MIT)
QLE, Snowflakes, slot machines, SLE...
Abstract: I'll introduce and explain the "quantum Loewner evolution", which is a variant of SLE in which one has a measurevalued driving function in place of a pointvalued driving function. This measure is closely related to the boundary measure of a Liouville quantum gravity surface, which is "explored" by the QLE. For certain parameters, there is a surprisingly close relationship between QLE and SLE. I'll explain what these ideas tell us about diffusion limited aggregation (DLA) and what they tell us about the metric space structure of the Brownian map. We'll also see how they relate to first passage percolation on random planar maps, and to both the "quantum gravity" KPZ and the "growth process" KPZ. There will be lots of pictures and animations. Everything in this talk is joint work with Jason Miller.

September 30
Alex Drewitz (Columbia)
Asymptotics of the critical parameter for level set percolation of the Gaussian free field
Abstract: We consider the Gaussian free field in Z^d, d>=3. It is known that there exists a nontrivial phase transition for its level set percolation; i.e., there exists a critical parameter h*(d) in [0,infinity) such that for h < h*(d) the excursion set above level h does have a unique infinite connected component, whereas for h > h*(d) it consists of finite connected components only. We investigate the asymptotic behavior of h*(d) as d>infinity and give some ideas on the proof of this asymptotics. Joint work with P.F. Rodriguez)

October 7
Yan Fyodorov (Queen Mary University of London)
Disordergenerated multifractals and Random Matrices: freezing phenomena and extremes
Abstract: I will start with discussing the relation between a class of disordergenerated multifractals and logarithmicallycorrelated random fields and processes. An important example of the latter is provided by the socalled "1/f noise" which, in particular, emerges naturally in studies of characteristic polynomials of CUE matrices. Extending the consideration to GUE setting reveals more processes of that type, in particular a special singular limit of the Fractional Brownian Motion. In the rest of the talk I will attempt to show how to use heuristic insights from Statistical Mechanics of disordered systems to arrive to a detailed conjectures about distributions of high and extreme values of logarithmically correlated processes and multifractals, including the absolute maximum of the Riemann zetafunction in intervals of the critical line.

October 17
Thursday, room E17133, 3pm4pm (special date, room and time)
Juerg Froehlich (ETH Zurich)
Quantum probability theory
Abstract: After a brief general introduction to the subject of quantum probability theory, quantum dynamical systems are introduced and some of their probabilistic features are described. On the basis of a few general principles  "duality between observables and indeterminates", "loss of information" and "entanglement generation"  a quantum theory of experiments and measurements is developed, and the "theory of von Neumann measurements" is outlined. Finally, a theory of nondemolition measurements is sketched, and, as an application of the Martingale Convergence Theorem, it is shown how facts emerge in nondemolition measurements.

October 21
Peter Forrester (University of Melbourne)
Some interrelations between random matrix ensembles
Abstract: In the early 1960's Dyson and Mehta found that the CSE relates to the COE. I'll discuss generalizations as well as other settings in random matrix theory in which beta relates to 4/beta.

October 28
Special full day event at MIT!
2nd Charles River Lectures on Probability and Related Topics
Details
Abstract: The Charles River Lectures on Probability and Related Topics will be hosted by the Massachusetts Institute of Technology. The lectures are jointly organized by Harvard University, Massachusetts Institute of Technology and Microsoft Research New England for the benefit of the greater Boston area mathematics community. The event features five lectures by distinguished researchers in the areas of probability and related topics.
This year's lectures will be delivered by:
 Martin Hairer (University of Warwick)
 Ioannis Karatzas (Columbia University)
 Elchanan Mossel (U.C. Berkeley)
 Assaf Naor (New York University)
 Balint Virag (University of Toronto)
For questions regarding the event, please contact charlesriverlectures2013@gmail.com.

November 4
David Wilson (Microsoft Research)
Local statistics of the abelian sandpile model
Abstract: We show how to compute local statistics of the abelian sandpile model on the square, hexagonal, and triangular lattices. The onesite marginals alone on the square lattice took more than 15 years to determine. We prove that on the square lattice, all local events are rational polynomials in 1/pi, while on the hexagonal and triangular lattices they are rational polynomials in sqrt{3}/pi. The proofs use the Cori and Le~Borgne version of Majumdar and Dhar's burning bijection between sandpiles to spanning trees, and the methods of Kenyon and Wilson for computing grove partition functions.

November 12
Tuesday, room E25111, at 4.15
Tim Austin (Courant Institute)
Exchangeable random measures
Abstract: Classical theorems of de Finetti, AldousHoover and Kallenberg describe the structure of exchangeable probability measures on spaces of sequences or arrays. Similarly, one can add an extra layer of randomness, and ask after exchangeable random measures on these spaces. It turns out that those classical theorems, coupled with an abstract version of the `replica trick' from statistical physics, give a structure theorem for these random measures also. This leads to a new proof of the DovbyshSudakov Theorem describing exchangeable positive semidefinite matrices, and has potential applications in the study of meanfield spin glasses.

November 1819
Special event at Harvard!
Ahlfors Lecture series delivered by Wendelin Werner (ETH Zurich)
Lecture I is November 18, 2013 from 4:155:15 pm in Harvard Science Center Hall A.
Lecture II is November 19, 2013 from 4:155:15 pm in Harvard Science Center Hall D.

November 25
Herbert Spohn (Munich Technical University)
Interacting Brownian motions in the KPZ universality class
Abstract: We discuss interacting Brownian motions in one dimension. Nearest neighbors interact through a drift depending only on their relative displacement. The reversible case is well studied with Gaussian fluctuations of order t^{1/4}. For the nonreversible case one expects nonGaussian fluctuations of order t^{1/3}. We explain recent results pointing towards this conjecture.
This is joint work with P.L. Ferrari, T. Sasamoto, and T. Weiss.

December 2
Gaetan Borot (Max Planck Institute, Bonn)
Asymptotics of multidimensional integrals arising in random matrix theory
Abstract: The beta ensembles of random matrix theory describe the statistical mechanics of N particles on the real line, repelling each other with Coulomb interaction, trapped in a potential V and coupled to an environment at temperature 1/β. I will present results about the allorder asymptotic expansion of the partition function and moments, as well as (the breakdown of) a central limit theorem fluctuations of linear statistics. The nature of the results depend on the topology of the locus of condensation of the particles in the large N limit. As a special case for β = 2  related to the hermitian 1matrix model , we can deduce allorder asymptotics of solutions of the Toda chain, and of (skew) orthogonal polynomials away from their zero locus. The theory to more general interactions between the particles provided they behave like Coulomb repulsion at short distances. This is based on joint works with Alice Guionnet, and current work including Karol Kozlowski.

December 9
Hao Wu (MIT)
On the conformally invariant growing mechanism in CLE4
Abstract: CLE4 is the collection of level lines of GFF. Miller and Sheffield give the first coupling between GFF and CLE4 in the way that loops in the CLE4 are the outmost \pm\lambdaheight level loop of the field. From the study of CLE4, Werner and me construct a time parameter for each loop in CLE4 such that the time parameter transforms in a conformally invariant way. From this construction of time parameter, Sheffield, Watson and me derive the second coupling between GFF and CLE4. In this talk, we will first give the background of SLE, CLE and GFF. And then, discuss the coupling between GFF and SLE4, the first and the second coupling between GFF and CLE4.
Semester/Year programs

January  March 2014
IHP trimester on Random Walks and Asymptotic Geometry of Groups, Paris, France

January  May 2014
CIMI trimester on Partial differential equations and probability, Toulouse, France

September 2013  June 2014
Institute for Advanced Studied Year Program on Nonequilibrium Dynamics and Random Matrices

January 5April 3, 2015
IHP trimester on Disordered Systems, Random Spatial Processes and their Applications, Paris, France
Schools

June 227, 2014
PIMS Summer School in Probability

July 718, 2014
MSRI Summer Graduate School on Stochastic Partial Differential Equations

July 14August 1, 2014
ICTP Summer College on Nonlinear Dynamics, Instabilities and Patterns in Classical and Quantum Systems
Conferences and Lecture Series

November 2122, 2013

January 2731, 2014

March 2629, 2014

May 1924, 2014
KPZ week, Toulouse, France.

July 28August 1, 2014
37th Conference on Stochastic Processes and their Applications, Buenos Aires, Argentina

August 611, 2014
7th International Conference on Stochastic Analysis and its Applications, Seoul, Korea

August 1321, 2014
International Congress of Mathematicians, Seoul, Korea

August 2226, 2014
International Conference on Quantum Probability and Related Topics, Seoul, Korea
Fall 2013 Organizers
 Alexei Borodin
 Ivan Corwin
 Vadim Gorin
 Jason Miller
 Scott Sheffield
 Charles Smart
 Omer Tamuz
 Hao Wu