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