Infosheet (January 17th, 2017) |
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).