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 subgroup-valued 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 20-22

  Special event at Boston University!

  Third annual Boston University -- Keio University Workshop

• 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 measure-valued driving function in place of a point-valued 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 non-trivial 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)

  Disorder-generated multifractals and Random Matrices: freezing phenomena and extremes

  Abstract: I will start with discussing the relation between a class of disorder-generated multifractals and logarithmically-correlated random fields and processes. An important example of the latter is provided by the so-called "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 zeta-function in intervals of the critical line.

• October 17

  Thursday, room E17-133, 3pm-4pm (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 non-demolition measurements is sketched, and, as an application of the Martingale Convergence Theorem, it is shown how facts emerge in non-demolition measurements.

• October 21

  Peter Forrester (University of Melbourne)

  Some inter-relations 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 one-site 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 E25-111, at 4.15

  Tim Austin (Courant Institute)

  Exchangeable random measures

  Abstract: Classical theorems of de Finetti, Aldous-Hoover 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 Dovbysh-Sudakov Theorem describing exchangeable positive semi-definite matrices, and has potential applications in the study of mean-field spin glasses.

• November 18-19

  Special event at Harvard!

  Ahlfors Lecture series delivered by Wendelin Werner (ETH Zurich)

  Lecture I is November 18, 2013 from 4:15-5:15 pm in Harvard Science Center Hall A.

  Lecture II is November 19, 2013 from 4:15-5:15 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 non-reversible case one expects non-Gaussian 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 all-order 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 1-matrix model -, we can deduce all-order 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\lambda-height 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 Non-equilibrium Dynamics and Random Matrices

• January 5-April 3, 2015

  IHP trimester on Disordered Systems, Random Spatial Processes and their Applications, Paris, France

Schools

• June 2-27, 2014

  PIMS Summer School in Probability

• July 7-18, 2014

  MSRI Summer Graduate School on Stochastic Partial Differential Equations

• July 14-August 1, 2014

  ICTP Summer College on Non-linear Dynamics, Instabilities and Patterns in Classical and Quantum Systems

Conferences and Lecture Series

• November 21-22, 2013

  Northeast Probability Seminar, CUNY

• January 27-31, 2014

  Rough Paths: Theory and Applications, UCLA

• March 26-29, 2014

  Seminar on Stochastic Processes, UCSD

• May 19-24, 2014

  KPZ week, Toulouse, France.

• July 28-August 1, 2014

  37th Conference on Stochastic Processes and their Applications, Buenos Aires, Argentina

• August 6-11, 2014

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

• August 13-21, 2014

  International Congress of Mathematicians, Seoul, Korea

• August 22-26, 2014

  International Conference on Quantum Probability and Related Topics, Seoul, Korea