Schedule for Winter 2011 Monday, November 29, 4:30 - 6:00, Jeff 102 Tim Harris (Queen's) Asymptotic Freeness of Independent Gaussian Random Matrices I will present a proof that independent Gaussian random matrices are asymptotically free.Monday, November 22, 4:30 - 6:00, Jeff 102 Emily Redelmeier (Queen's) Genus expansion for Haar-distributed orthogonal matrices, Part II I will present some results on Haar-distributed orthogonal matrices connected with second-order freeness.
Monday, November 15, 4:30 - 6:00, Jeff 102 Emily Redelmeier (Queen's) Genus expansion for Haar-distributed orthogonal matrices I will present some results on Haar-distributed orthogonal matrices connected with second-order freeness.
Monday, November 8, 4:30 - 6:00, Jeff 102 Michael Brannan (Queen's) Quantum symmetries and a strong form of Haagerup's inequality, Part II.
Monday, November 1, 4:30 - 6:00, Jeff 102 Michael Brannan (Queen's) Quantum symmetries and a strong form of Haagerup's inequality. Haagerup's inequality is an important inequality in the field of operator algebras, having many interesting and surprising applications. In this talk we will give an overview of Haagerup's inequality and its connection to free probability theory. We will then go on to outline the proof of the following new result: Consider an n-tuple of operators in a C*-probability space whose joint *-distribution possesses a certain degree quantum symmetry - namely we require that the *-distribution be invariant under the operation of free complexification and the natural coaction of the hyperoctahedral quantum group. Then it follows that the non-self-adjoint operator algebra generated this family always satisfies a strong form of Haagerup's inequality. We will conclude by showing how this result generalizes work of Kemp and Speicher (2007) on strong Haagerup inequalities for *-free, identically distributed families of R-diagonal operators, and by discussing some applications to strong Haagerup inequalities for free unitary quantum groups.
Wednesday October 27, 3:30 - 5:00, Jeff 102 James Mingo Queen's Univ. The Moebius Function and the Weingarten Function I will continue from the previous week.
Monday October 18, 4:30 - 6:00, Jeff 102 James Mingo Queen's Univ. The Moebius Function and the Weingarten Function Two of the most important functions in free probability are the Moebius function and the Weingarten function. The Moebius function is used to write cumulants in terms of moments and the Weingarten function is used to calculate integrals against the Haar measure of the unitary group U(n). I will explain the background to these functions and show how they are related by a simple equation. This is joint work with Roland Speicher.
Monday September 27, 4:30 - 6:00, Jeff 102 Octavio Arizmendi Echegaray, (Queen's) Convolution on k-divisible Non Crossing Partitions and Free Probability In this talk we will explain in detail some nice properties of the convolution with the zeta function on the k-divisible lattice of Non Crossing Partitions and how this relate with the convolution of the zeta function on the whole Non-Crossing Partitions. As a consequence of this we can derive a nice formula for the free cumulants the x^{k} in terms of the free cumulants of x, when x is a k-divisible element. Finally, using this formulas we give results on free infinite divisibility, in particular we show that the square of a freely infinitely divisible element is also freely infinitely divisibleIn particular on Free Infinite Divisibility. Monday September 20, 4:30 - 6:00, Jeff 102 Carlos Vargas (Queen's) Solving a Random Matrix Problem using Operator-Valued Free Probability We describe the asymptotic distribution of sums of random matrices of the form B = sum_k R_k C_k T_k C_k^* R_k, where the C_k's are square random matrices of different sizes with independent complex Gaussian entries and the R_k's and T_k's are suitable deterministic matrices. By amalgamating over the algebra generated by our deterministic matrices, we show that the summands are free over this algebra and use this fact to compute the operator-valued Cauchy transform. This relies on the asymptotic circularity of the square random matrices
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