University of Ottawa Analysis Seminar
Time and Location
The analysis seminar meets roughly once per week during the academic year. The time and room for the Winter semester will be Fridays 1:10pm  2:10pm, FSS 7003.
To schedule a talk, please contact Charles Starling
Previous years:
Date  Speaker  Title 
Time and Room 
Jan 27 
Saeid Molladavoudi, uOttawa 
Cohomological invariants for Abelian symplectic quotients of
pure rqubits
Abstract:
Symmetries are ubiquitous in natural phenomena and also in
their mathematical descriptions and according to a general principle in
Mathematics, one should exploit a symmetry to simplify a problem
whenever possible. In this talk, we focus on elimination of continuous
symmetries from multiparticle quantum systems and discuss that the
existing methods equip us with a powerful set of tools to compute
geometrical and topological invariants of the resulting reduced spaces.
As an intermediate step, we consider the maximal torus subgroup of the
compact Lie group of Local Unitary operations K and elaborate on the
symmetry reduction procedure and use methods from symplectic geometry
and algebraic topology to obtain some of the topological invariants of
these relatively wellbehaving quotients for multiparticle systems
containing r qubits. More precisely, by fixing the relative phases of
isolated r qubits and then varying them inside their domain in an
rdimensional hypercube, we explain how to obtain cohomology rings and a
recursive wallcrossing algorithm to compute cohomological pairings over
the corresponding Abelian symplectic quotients. We elaborate on an
explicit example with two qubits and discuss further implications in
quantum information theory.

1:10pm2:10pm FSS 7003 
Feb 3 
Brice Mbombo, uOttawa 
Dynamic of the group of self homeomorphisms of the Poulsen simplex
Abstract:
After a gentle introduction to the KechrisPestovTodorcevic correspondence for Polish groups, we will present as application some dynamical properties of the group of self homeomorphisms of the Poulsen simplex. No specialized knowledge is assumed.
This is a joint work with Dana Bartošová (Carnegie Melon University), Jordi LópezAbad (Université Paris VII, France), and Martino Lupini (Caltech)

1:10pm2:10pm FSS 7003 
Feb 10 
None 


Feb 17 
None 

1:10pm2:10pm FSS 7003 
Feb 24 
Reading break 


Mar 3 
Thierry Giordano, uOttawa 
Old and new examples of approximate transitive actions
Abstract:
In 1981, A. Connes and E.J. Woods introduced the definition of an approximate transitive (AT) action of a group G to characterize the flow of weights of the ArakiWoods factors of type III. A few years later they proved that the asymptotic boundary of a (time dependent) random walk on G is an amenable and AT space.
In this talk, I will mainly review the notion of approximate transitivity and present some new developments.

1:10pm2:10pm FSS 7003 
Mar 10 
Thierry Giordano, uOttawa 
More on AT actions

1:10pm2:10pm FSS 7003 
Mar 17 
None 

1:10pm2:10pm FSS 7003 
Mar 24 
None 

1:10pm2:10pm FSS 7003 
Mar 31 
Johannes Cuno, uOttawa 
Free groups and the Hanna Neumann conjecture
Abstract:
Let G be a group and let A and B be finitely generated subgroups of G. In general, the intersection A ∩ B need not be finitely generated any more. But if G is a free group, it is. Here the question arises whether the rank of A ∩ B can be bounded in terms of the ranks of A and B. In 1956/1957, Hanna Neumann gave such a bound and conjectured that it can be improved by removing the factor 2. This problem became known as the Hanna Neumann Conjecture and it remained unsolved for more than 50 years. In 2011, Joel Friedman and Igor Mineyev independently gave proofs of the so called Strengthened Hanna Neumann Conjecture, which implies the classical one.
In this talk, I will give an introduction to free groups and illustrate some important theorems. Then, I will focus on the classical Hanna Neumann Conjecture and give a surprisingly elementary proof developed by Warren Dicks and Igor Mineyev. The talk is designed to address a broad mathematical audience. But, let me underline: It is not about my own research! It is about a brilliant idea that nails an old problem, and deserves to be communicated.

1:10pm2:10pm FSS 7003 
Date  Speaker  Title 
Time and Room 
Sept 22 
Hun Hee Lee Seoul National University 
Some modified Fourier algebras are operator algebras
Abstract:
In this talk we will introduce a way of modifying Fourier algebras on compact groups and discrete groups. We examine whether these modified algebras are completely isomorphic to operator algebras and explain its connection to the real dimension of the compact connected Lie group and the growth rate of certain finitely generated groups.

4:00pm5:00pm, KED B015 
Sep 28 
Charles Starling uOttawa 
Groupoids
Abstract:
Groupoids are central to the study of C*algebras, dynamical systems, and associative algebras. In this expository talk I present the basics of topological groupoids with focus put on some important examples. No specialized knowledge is assumed.

2:40pm3:40pm, DMS 11161 
Oct 5 
David Handelman uOttawa 
Ordered cohomology of directed graphs, topological dynamical systems, and a modicum of C*algebras
Abstract:
Minimal actions on Cantor sets have been heavily studied and classified.
Much less is known about nonminimal actions. In general, these can be
built from toy actions arising from finite directed graphs. Applying the
preordered K_{0}functor to the crossed products yields ordered
cohomology for the both the graphs, and the dynamical systems. We discuss
the connections, and in particular, what it means for graphs to be
cohomologically trivial, in the sense that the ordered groups are
simplicial (whatever that means). It follows (eventually) from results on
these that certain dimension groups, big and small, cannot be realized in
the general dynamical system setting. This is joint with Mike Boyle. 
2:40pm3:40pm, DMS 11161 
Oct 12 
Vadim Kaimanovich uOttawa 
Lamenable actions
Abstract:
The notion of amenability was first extended from groups to transitive group actions by Greenleaf (1969) by requiring that there exist an invariant mean on the action space. However, shortly thereafter this notion was eclipsed by Zimmer's definition (which is in a sense complementary to Greenleaf's one) and remained almost forgotten until fairly recently.
Amenability of a transitive action of a finitely generated group is
equivalent to amenability of the associated Schreier graph, and
the growing interest in properties of Schreier graphs has made Greenleaf's definition popular again during the last decade.
Inspired by a recent paper by Juschenko and Zheng on the Liouville
property for Schreier graphs, I will introduce yet another version of
amenability for actions and discuss its basic properties.

2:40pm3:40pm, DMS 11161 
Oct 19 
Jason Crann Carleton 
Introduction to completely positive maps
Abstract:
This talk will be the first in a learning seminar series on order zero completely positive maps and their applications in C*algebras. After discussing motivations, I will introduce the notion of complete positivity and present various structural properties and examples, focusing mainly on finitedimensional C*algebras. 
2:40pm3:40pm, DMS 11161 
Oct 26 

Reading Week 

Nov 2 
Johannes Cuno uOttawa 
BaumslagSolitar groups and around
Abstract:
Being new to the University of Ottawa, I would like to use this occasion to outline some of my past and present research. After addressing a couple of questions from combinatorial group theory, I shall focus on BaumslagSolitar groups. Their geometry will allow us to study random walks on these groups and to identify the associated Poisson boundary. The talk shall conclude with musings about other boundaries. It is designed for a broad audience, no specialized knowledge is assumed.

2:40pm3:40pm, DMS 11161 
Nov 9 
Jason Crann, Carleton 
Stinespring's Representation Theorem
Abstract:
Continuing from last time, we will discuss structural properties of completely positive maps, mainly through Stinespring's representation theorem and its applications. Examples will be drawn from the class of Schur maps, both on matrix algebras and group C*algebras.

2:40pm3:40pm, DMS 11161 
Nov 16 
Elisabeth Fink, uOttawa 
Amenability and Asymptotic Cones
Abstract:
Asymptotic cones of groups are certain limit spaces capturing 'big scale' phenomena of the Cayley graph of a group. In this talk I will discuss an elementary amenable group that is a direct limit of hyperbolic groups, where every of its asymptotic cones has cut points, the first known example of this kind. This will be done by algebraically exhibiting Morse geodesics in those groups, which can be seen as certain hyperbolic directions. I will illustrate with examples of other groups and their asymptotic cones why this is a surprising phenomenon. Further, I will discuss ongoing research in this project and related groups.

2:40pm3:40pm, DMS 11161 
Nov 23 
Jason Crann, Carleton 
Applications of Stinespring Representations
Abstract:
We finish our introduction to completely positive maps with several applications of Stinespring's representation theorem. In particular, we show that a complete order isomorphism of C*algebras is necessarily a *isomorphism. We illustrate the material with important examples from operator algebras and quantum information theory.

2:40pm3:40pm, DMS 11161 
Nov 30 
Luiz Cordeiro, uOttawa 
Determining a compact space via orthogonal functions
Abstract:
The connections between topological and algebraic structures have been topics of ongoing interest for at least 80 years, since Stone's work on representations of Boolean algebras. Since then, several results of a similar nature have been proven, and the theory continues to be developed to this day. I will present a general, yet elementary, approach to the question of determining a compact space in terms of its continuous functions and the orthogonality relation, which generalizes (at least part of) many of the classical, as well as some recent, results in the area.

2:40pm3:40pm, DMS 11161 
