Infosheet (February 13th, 2018)

Queen's University - Department of Mathematics and Statistics


Tuesday, February 13

Seminar in Free Probability and Random Matrices

Time: 3:30 p.m.

Place: Jeffery 319

Speaker: Jamie Mingo

Title: The Infinitesimal Law of the GOE, Part II

Abstract Attached

Wednesday, February 14

Department Colloquium

Time: 3:30 p.m.

Place: Jeffery 234

Speaker: Qiang Zeng, Northwestern University

Title: Replica symmetry breaking for mean field spin glass models

Abstract Attached

Thursday, February 15

Math Club

Time: 5:30 p.m.

Place: Jeffery 118

Speaker: Mike Roth

Title: The Metropolis-Hastings Algorithm

Abstract Attached

Friday, February 16

Department Colloquium

Time: 2:30 p.m.

Place: Jeffery 234

Speaker: Catherine Pfaff

Title: A Nielsen-thurston inspired story of iterating free group automorphisms and efficiently deforming graphs

Abstract Attached

Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.


Tuesday, February 13, 3:30 p.m. Jeffery 319

Seminar in Free Probability and Random Matrices

Speaker: Jamie Mingo

Title: The Infinitesimal Law of the GOE, Part II

Abstract: If X_N is the N x N Gaussian Orthogonal Ensemble (GOE) of random matrices, we can expand E(tr(X_N^n)) as a polynomial in 1/N, often called a genus expansion. Following the celebrated formula of Harer and Zagier for the GUE, Ledoux (2009) found a five term recurrence for the coefficients of E(tr(X_N^n)). We show that the coefficient of 1/N counts the number of non-crossing annular pairings of a certain type.

Our method is quite elementary. A similar formula holds for the Wishart ensemble. This identification is related to the theory of infinitesimal freeness of Belinschi and Shlyakhtenko.

Seminar website: http://www.mast.queensu.ca/~mingo/seminar/


Wednesday, February 14, 3:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Qiang Zeng

Title: Replica symmetry breaking for mean field spin glass models

Abstract: In statistical physics, the study of spin glasses was initialized to describe the low temperature

state of a class of magnetic alloys in the 1960s. Since then spin glasses have become a paradigm for highly complex disordered systems. Mean field spin glass models were introduced as an approximation

of the physical short range models in the 1970s. The typical mean field models include the Sherrington-Kirkpatrick (SK) model, the (Ising) mix p-spin model and the spherical mixed p-spin model.
Starting in 1979, the physicist Giorgio Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking (RSB), which allowed him to predict a solution for the SK model by

breaking the symmetry of replicas infinitely many times at low temperature. This is known as full-step

replica symmetry breaking (FRSB). In this talk, we will show that Parisi's FRSB prediction holds at zero temperature for the more general mixed p-spin model. As a consequence, at positive temperature the level of RSB will diverge as the temperature goes to zero. On the other hand, we will show that there exist two-step RSB spherical mixed spin glass models at zero temperature, which are the first examples beyond the replica symmetric, one-step RSB and FRSB phases.
This talk is based on joint works with Antonio Auffinger (Northwestern University) and Wei-Kuo Chen (University of Minnesota).


Thursday, February 15, 5:30 p.m. Jeffery 118 - Math Club

Speaker: Mike Roth

Title: The Metropolis-Hastings Algorithm

Abstract: The Metropolis-Hastings algorithm (and its variations) is one of the most widely used methods in scientific computing. Roughly, its purpose is to produce a sequence of numbers distributed according to a given probability distribution.

This talk will explain the most basic version of the algorithm, as well as an application to decoding substitution codes.


Friday, February 16, 2:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Catherine Pfaff

Title: A Nielsen-thurston inspired story of iterating free group automorphisms and efficiently deforming graphs

Abstract: While many fundamental contributions to the study of outer automorphisms of free groups date back to the early 20th century, the real explosion of activity in the field came with two much more recent developments: the definition by Culler and Vogtmann of the deformation space of metric graphs on a surface, namely Outer Space, and the development by Bestvina, Feighn, and Handel of a train track theory for outer automorphisms of free groups. The explosion was a result of a new ability to study free group outer automorphisms using generalizations of techniques developed to study surface homeomorphisms (mapping classes) via their action on the deformation space of metrics on the surface (Teichmuller space). In our talk, we focus specifically on a Nielsen-Thurston inspired story jointly studying:

  1. outer automorphism conjugacy class invariants obtained by iteratively applying the automorphisms and
  2. geodesics in Culler-Vogtmann Outer Space.

Contact Info

Department of Math & Stats
Jeffery Hall, 48 University Ave.
Kingston, ON Canada, K7L 3N6
Phone: (613) 533-2390
Fax: (613) 533-2964
mathstat@mast.queensu.ca
Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm

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