The Random Matrix and Probability Theory Seminar will be every Wednesday from 3pm4pm in CMSA Building, 20 Garden Street, Room G10.
The schedule will be updated as details are confirmed.
Date  Name  Title/Abstract 
92717  Herbert Spohn, Technische Universität München  Hydrodynamics of integrable classical and quantum systems
Abstract: In the cold atoms community there is great interest in developing Eulertype hydrodynamics for onedimensional integrable quantum systems, in particular with application to domain wall initial states. I provide some mathematical physics background and also compare with integrable classical systems. 
102317
*12:001:00pm, Science Center 232* 
Madhu Sudan, Harvard SEAS

General Strong Polarization
A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of errorcorrecting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the “polarization” of a “bounded” martingale. A bounded martingale, X_0,…,X_t,… is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the aforementioned algorithmic challenge. In this talk I will introduce the concepts of polarization and strong polarization. Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so). Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra. 
102517
*2:004:00pm*

Subhabrata Sen (Microsoft and MIT)
Noga Alon,(Tel Aviv University)

Subhabrata Sen, “Partitioning sparse random graphs: connections with meanfield spin glasses”
Abstract: The study of graphpartition problems such as Maxcut, maxbisection and minbisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cutsizes on sparse Erd\ ̋{o}sR\'{e}nyi and random regular graphs. Based on joint work with Aukosh Jagannath. Noga Alon, “Random Cayley Graphs” Abstract: The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given group with a prescribed number of generators. Several intriguing questions that remain open will be mentioned as well. 
11117
*2:004:00pm*

Kay Kirkpatrick (Illinois)
and WeiMing Wang (CNRS)

Kay Kirkpatrick, Quantum groups, Free ArakiWoods Factors, and a Calculus for Moments
Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free ArakiWoods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we’ll mention another quantum central limit theorem for BoseEinstein condensation and work in progress. WeiMin Wang, Quasiperiodic solutions to nonlinear PDE’s Abstract: We present a new approach to the existence of time quasiperiodic solutions to nonlinear PDE’s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser. 
11817  Elchanan Mossel  Optimal Gaussian Partitions.
Abstract: How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution. The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory. I will survey the little we know about this problem and the major open problems in the area. 
111017
*12pm SC 232*

Zhe Wang (NYU)

A Driven Tagged Particle in Onedimensional Simple Exclusion Process
Abstract: We study the longtime behavior of a driven tagged particle in a onedimensional nonnearest neighbor simple exclusion process. We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes. 
111517
*4:005:00pm* *G02*

Daniel Sussman (BU)

Multiple Network Inference: From Joint Embeddings to Graph Matching
Abstract: Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiplenetwork framework remains a relatively underexplored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, facetoface interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, we’ll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching.

112017
*Monday 12:001:00pm* 
Yue M. Lu
(Harvard) 
Asymptotic Methods for HighDimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs
Abstract: Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very highdimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widelyused spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and meanfield limits to analyze nonconvex optimization algorithms for highdimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with highdimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices.

112917  David Gamarink (MIT)  (Arguably) Hard on Average Constraint Satisfaction Problems
Abstract: Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by nonconstructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAEKSAT problem, the problem of finding a largest submatrix of a random matrix, and a highdimensional sparse linear regression problem in statistics.
Joint work with WeiKuo Chen, Quan Li, Dmitry Panchenko, Mustazee Rahman, Madhu Sudan and Ilias Zadik. 
12617
*2:004:00pm* 
Philippe Rigollet (MIT)
23 pm & Ankur Moitra (MIT) 34 pm

Philippe Rigollet (MIT), Exact Recovery in the Ising Block Model
Abstract: Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated CurieWeiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples. This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute). Ankur Moitra (MIT), A New Approach to Approximate Counting and Sampling Abstract: Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higherorder constraints.

121417  TBD  