Events - May 2018

Daniel Pepper, Department of Pure Mathematics, University of Waterloo

In this learning seminar we will study some basic facts about the free probability analogue of the Brownian motion, and about how one can do stochastic integration against the free Brownian motion.  The framework used will be the one of a C*-probability space.  The main reference followed will be a paper by P. Biane and R. Speicher titled "Stochastic calculus with respect to free Brownian motion and analysis on Wigner space" (in Probability Theory and Related Fields, 1998).

M3 3103

Jorge Galindo, Universitat Jaume I

"\ell_1-sequences and Arens regularity of the Fourier algebra"

The Fourier algebra A(G) of a locally compact Abelian group G is the algebra of functions on G whose Fourier transforms are integrable on the dual group \widehat{G}. When G is not commutative, the definition of A(G) is more sophisticated and produces an often intriguing Banach Algebra that has interest from the perspectives of Harmonic Analysis and Operator Theory.

Jonathan Herman, Department of Pure Mathematics, University of Waterloo

"Weak Moment Maps in Multisymplectic Geometry"

We introduce the notion of a `weak (homotopy) moment map' associated to a Lie algebra action on a multisymplectic manifold.

We use weak moment maps to extend Noether's theorem from Hamiltonian mechanics by exhibiting a correspondence between multisymplectic conserved quantities and continuous symmetries on a multi-Hamiltonian system.

Yifan Yang, National Taiwan University

"Equations of Shimura curves"

Shimura curves are generalizations of classical modular curves. Because of the lack of cusps on Shimura curves, there are very few explicit methods for Shimura curves. In this talk, we will introduce Borcherds forms and use them to determine the equations of Shimura curves. The construction of Borcherds forms is done by solving certain integer programming problems. This is a joint work with Jia-Wei Guo.

MC 5403

Josh Hews, Department of Pure Mathematics, University of Waterloo

"Algorithms for 3-Manifolds"

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"Degree invariant functions and Martin's Conjectures"

We will continue the proof we started for the special case of Martin's conjecture.  That special case result says: Assuming the Axiom of Determinacy, a uniformly degree invariant function that is not increasing on a cone must be constant on a cone. 

MC 5403

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"Degree invariant functions and Martin's Conjectures"

We will go through a theorem which proves a special case of one of Martin's conjectures about degree (Turing) invariant functions. The theorem says: Assuming the Axiom of Determinacy, a uniformly degree invariant function that is not increasing on a cone must be constant on a cone. The theorem is about a uniformly degree invariant function while the conjecture is about any degree invariant function, not necessarily uniformly.

Janez Bernik, University of Ljubljana

"Quasi-filiform Lie algebras of maximum length revisited"