# Queen's University - Department of Mathematics and Statistics

 Tuesday, January 17 Seminar in Free Probability and Random Matrices Time: 2:30 p.m. Place: Jeffery 222 Speaker: Jamie Mingo Title: Free Probability of Type B Abstract Attached Tuesday, January 17 Dynamics Seminar Time: 3:30 p.m. Place: Jeffery 422 Speaker: Thomas Barthelmé Title: A Lyapunov spectrum for convex functions Abstract Attached Wednesday, January 18 Curves Seminar Time: 3:30 p.m. Place: Jeffery 422 Speaker: Mike Roth Title: Quotients of affine varieties by reductive groups Abstract Attached Friday, January 20 Number Theory Seminar Time: 10:30 a.m. Place: Jeffery 422 Speaker: M. Ram Murty Title: Euclidean Rings and Wieferich Primes Abstract Attached Friday, January 20 Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 Speaker: Maxime Theillard, University of California San Diego Title: High-fidelity simulations of complex fluid flows Abstract Attached Monday, January 23 Department Colloquium Time: 4:30 pm Place: Jeffery 234 Speaker: Eric Foxall, Arizona State University Title: The partner model: critical and non-critical behaviour 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, January 17, 2:30 p.m. Jeffery 222

Seminar in Free Probability and Random Matrices

Speaker: Jamie Mingo

Title: Free Probability of Type B

Abstract: Since Voiculescu introduced free independence 35 years ago, many variants have appeared: Boolean, monotone, type B, second order, higher order, real, quaternionic, infinitesimal, and bi-free independence (plus combinations of the above) to name a few. Most of the constructions are given combinatorially, but some have an interpretation in terms of analytic functions. I will discuss the 2003 paper of Biane, Goodman, and Nica, which introduced freeness of type B.

This will be the first of two lectures. This lecture will describe free cumulants of type B and type B freeness. The second lecture will explain how the hyperoctahedral group comes into play and hence why this is called type B freeness.

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

Tuesday, January 17, 3:30 p.m. Jeffery 422 - Dynamics Seminar

Speaker: Thomas Barthelmé

Title: A Lyapunov spectrum for convex functions

Abstract: In his last article before retiring, Mickaël Crampon discovered the surprising fact that strictly convex functions admit a sort of Lyapunov spectrum: Roughly speaking, if f is a strictly convex function, one can define a number $\alpha(v)$ that captures the Hölder coefficient of f in the direction v, then $\alpha(v)$ will take only finitely many different values and there is a splitting (and a filtration) of the tangent space associated to these values.

I will talk about where this result comes from (spoiler: it comes from the dynamics of the geodesic flow of Hilbert geometries), and some of the questions that Mickaël left open for the world to wonder about.

Wednesday, January 18, 3:30 p.m. Jeffery 422 - Curves Seminar

Speaker: Mike Roth

Title: Quotients of affine varieties by reductive groups

Abstract: We will study the quotient of affine varieties by reductive algebraic groups.

Friday, January 20, 10:30 a.m. Jeffery 422 - Number Theory Seminar

Speaker: M. Ram Murty

Title: Euclidean Rings and Wieferich Primes

Abstract: It is conjectured that if the ring of integers of a real quadratic field is a PID, then it is in fact a Euclidean domain. The conjecture is known under the assumption of the generalized Riemann
hypothesis (GRH). We replace the GRH with another hypothesis about Wieferich primes, namely that
the number of primes p < x such that 2^{p-1} = 1(mod p^2) is o(x/log^2 x). We show that this implies the conjecture. This is joint work with K. Srinivas and M. Subramani.

Friday, January 20, 2:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Maxime Theillard

Title: High-fidelity simulations of complex fluid flows

Abstract: The remarkable properties of complex fluids are the consequence of a subtle interplay between multiple physics, occurring on different length and time scales and often involving deformable interfaces. Numerically, all these characteristics make these flows extremely challenging to simulate. The numerical approach I will present in this talk is built on an incompressible fluid solver using adaptive Octree/Quadtree grids, which are highly effective in capturing disparate length scales. Designed as a stable projection method where viscous effects are treated implicitly, our solver was shown to be unconditionally stable. First, I will show how the method can be extended to simulate non-miscible two-phase flows. In this novel approach, the interface and continuity equations are treated in a sharp manner and by using a modified pressure correction projection method we were able to alleviate the standard time step restriction incurred by capillary forces. These properties make our framework a robust tool to simulate challenging single- and two-phase flow problems. Second, I will focus on another type of complex fluids: confined active suspensions, of which a bath of swimming microorganisms is a paradigmatic example. I will detail how our simulation engine was used to model such flows and present some numerical examples. Specifically I will show how collective behavior and spontaneous flowing states can emerge from hydrodynamics interactions between swimmers and analyze the influence of the confining geometry has on these dynamics.

Monday, January 23, 4:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Eric Foxall

Title: The partner model: critical and non-critical behaviour

Abstract: We consider a stochastic SIS model of infection spread that incorporates non-permanent, monogamous partnerships. Each of N individuals is either healthy or infectious, and infection can only be transmitted between partnered individuals. Normalizing the recovery rate to 1, we identify a threshold value of the transmission rate, as a function of the partnership formation and dissolution rates, below which the infection vanishes within O(log N) time, and above which it survives for at least e^{cN} time for constant c, approaching a unique endemic equilibrium. At the threshold value, the infection survives for order of sqrt{N} time. Away from the threshold value, the dynamics for large N approach solutions to a set of ordinary differential equations describing the proportion of each of the five types of singles and partnered pairs, while at the threshold value, a different rescaling leads to a one-dimensional stochastic differential equation.

Joint work with Rod Edwards, Pauline van den Driessche (non-critical behaviour) and Anirban Basak, Rick Durrett (critical behaviour).

### 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