Fall 2011

Schedule for Winter 2012 Monday,December 5, 4:30-6:00, Jeff 222 Jamie Mingo, (Queen's) Second Order R-diagonal Operators, II Nica and Speicher introduced an important class of operators they called R-diagonal. This is a class that includes non-normal operators but which have tractable spectral theory. I will discuss what is known about these operators and then some new work with Octavio Arizmendi on how to extend the results of Nica and Speicher to the second order case.Monday,

November 28, 4:30-5:30, Jeff 422 Jamie Mingo, (Queen's) Second Order R-diagonal Operators Nica and Speicher introduced an important class of operators they called R-diagonal. This is a class that includes non-normal operators but which have tractable spectral theory. I will discuss what is known about these operators and then some new work with Octavio Arizmendi on how to extend the results of Nica and Speicher to the second order case.Monday,

November 21, 5:00 - 6:30, Jeff 422 Mihai Popa, (Queen's) Non-Commutative Functions: Basic Theory and Applications in Free Probability, Part II The lecture will present the basics of non-commutative functions calculus together with some motivation from free probability. We will emphasize the properties of operational distributions and the use of the non-commutative Cauchy transform.Monday,

November 14, 4:30 - 6:00, Jeff 422 Mihai Popa, (Queen's) Non-Commutative Functions: Basic Theory and Applications in Free Probability, Part II The lecture will present the basics of non-commutative functions calculus together with some motivation from free probability. We will emphasize the properties of operational distributions and the use of the non-commutative Cauchy transform.Monday,

November 7, 4:30 - 6:00, Jeff 422 Mihai Popa, (Queen's) Non-Commutative Functions: Basic Theory and Applications in Free Probability The lecture will present the basics of non-commutative functions calculus together with some motivation from free probability. We will emphasize the properties of operational distributions and the use of the non-commutative Cauchy transform.Monday,

October 31, 4:00 - 5:30, Jeff 422 Termeh Kousha, (U. of Ottawa) Asymptotic behaviour and moderate deviation principle for the maximum of a Dyck path By using a new representation of the Catalan numbers, relying on the spectral properties of an associated adjacency matrix, we ﬁnd the distribution of the maximum of Dyck path for the case where the length of the Dyck path is proportional to the square root of the height. We also consider other cases and ﬁnd moderate and large deviation principles for the law of the maximum of random Dyck path for those cases.Monday,

October 24, 4:30 - 6:00, Jeff 422 Michael Hartz, (Waterloo) Extremal extensions for families of Hilbert-space operators Extension theorems are important tools in the study of operators on Hilbert spaces. Examples include the fact that every isometry on a Hilbert space can be extended to a unitary operator and the famous Sz.-Nagy dilation theorem for contractions. One is not only interested in extension results for single operators, but also for operator tuples. Jim Agler's theory of families provides a general framework for the search of extension theorems. In this talk, I will introduce the theory of families. Moreover, I will present applications of this theory to two families of commuting tuples of operators due to S. Richter and C. Sundberg. The first family consists of all commuting spherical isometries, that is commuting tuples (T_{1},... ,T_{n}) that satisfy ∑_{i=1}^{ n}T_{i}* T_{i}= 1, the second is the family of all commuting spherical contractions, that is commuting tuples (T_{1},... ,T_{n}) with Σ_{i=1}^{n}T_{i}* T_{i}≤ 1. As a consequence, we will obtain a previously known theorem by Athavale concerning the joint subnormality of commuting spherical isometries, as well as an extension theorem for commuting spherical contractions due to Müller-Vasilescu and Arveson.Monday,

September 12, 4:30 - 6:00, Jeff 202 Mike Brannan (Queen's) On the von Neumann algebras associated to quantum permutation groups In 1998, Shuzhou Wang showed that the classical permutation group S_N (on N letters) admits a natural counterpart in the category of compact quantum groups. We call this quantum version of S_N the quantum permutation group. In this talk, we will give an intuitive introduction to the quantum permutation groups, and discuss some of their probabilistic and operator algebraic properties. In particular, we will focus on the reduced von Neumann algebras associated to these quantum groups. For N < 5, an explicit description of these von Neumann algebras is known. On the other hand, for N at least 5, very little is known about these von Neumann algebras. We will show that for N at least 8, these von Neumann algebras are II_1 factors (i.e., have trivial centre), which moreover have the Haagerup approximation property.

Previous Schedules

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