# Seminar on Free Probability and Random Matrices Winter 2016

## Organizer: J. Mingo <!-- // // format date as dd-mmm-yy // example: 12-Jan-99 // function date_ddmmmyy(date) { var d = date.getDate(); var m = date.getMonth() + 1; var y = date.getYear(); // handle different year values // returned by IE and NS in // the year 2000. if(y >= 2000) { y -= 2000; } if(y >= 100) { y -= 100; } // could use splitString() here // but the following method is // more compatible var mmm = ( 1==m)?'Jan':( 2==m)?'Feb':(3==m)?'Mar': ( 4==m)?'Apr':( 5==m)?'May':(6==m)?'Jun': ( 7==m)?'Jul':( 8==m)?'Aug':(9==m)?'Sep': (10==m)?'Oct':(11==m)?'Nov':'Dec'; return "" + (d<10?"0"+d:d) + "-" + mmm + "-" + (y<10?"0"+y:y); } // // get last modified date of the // current document. // function date_lastmodified() { var lmd = document.lastModified; var s = "Unknown"; var d1; // check if we have a valid date // before proceeding if(0 != (d1=Date.parse(lmd))) { s = "" + date_ddmmmyy(new Date(d1)); } return s; } // // finally display the last modified date // as DD-MMM-YY // document.write( "Last modified on " + date_lastmodified() ); // -->   Schedule for Current Term

Thursday, September 6, 2:30 - 4:00, Jeff 222
Mario Diaz (Queen's)
On the Fluctuations of Block Gaussian Matrices, IV
This is a continuation of my previous talk.
Thursday, September 1, 1:30 - 3:00, Jeff 222
Mario Diaz (Queen's)
On the Fluctuations of Block Gaussian Matrices, III
This is a continuation of my previous talk.
Thursday, August 30, 1:30 - 3:00, Jeff 222
Mario Diaz (Queen's)
On the Fluctuations of Block Gaussian Matrices, II
This is a continuation of my previous talk.
Thursday, August 25, 1:30 - 3:00, Jeff 222
Mario Diaz (Queen's)
On the Fluctuations of Block Gaussian Matrices
In this talk we will extend a theorem of Mingo and Nica to compute the matricial second-order Cauchy transform of matricial-valued semicircular elements. Then, the fluctuations of block Gaussian random matrices will be obtained using this transform. This is joint work with Serban Belinschi and Jamie Mingo.
Wednesday, June 22, 3:30 - 5:00, Jeff 319
Octavio Arizmendi (CIMAT, Guanajuato)
The exponential map in non-commutative probability
The wrapping transformation W is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution operation. We show that on a large class L of measures, W also transforms the three non-commutative convolutions—free, Boolean, and monotone—to their multiplicative counterparts. Moreover, the restriction of W to L preserves various qualitative properties of measures and triangular arrays. We use these facts to give short proofs of numerous known, and new, results about multiplicative convolutions. This is joint work with Michael Anshelevich.
Wednesday, April 6, 1:30 - 3:00, Jeff 319
Mario Diaz (Queen's)
Analytic Properties of Certain Two-Variables Cauchy Transforms
In this talk we will present some analytic properties of certain two-variables Cauchy transforms. We will also discuss how these properties are related to questions about the existence of certain second-order Cauchy transforms.
Friday, April 1, 10:00 - 11:30, Jeff 222
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness, Hadamard matrices, and signed permutation matrices, III.
This talk will conclude my presentation of my results on second order freeness.
Thursday, March 17, 10:00 - 11:30, Jeff 222
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness, Hadamard matrices, and signed permutation matrices, II.
In this talk, we first show how to calculate the joint distribution of the entries of a uniformly distributed signed permutation matrix. Then, we explore the idea of using Hadamard matrices and uniformly distributed signed permutation matrices to deliver asymptotic freeness of second order. This is a continuation from March 10.
Thursday, March 10, 10:00 - 11:30, Jeff 222
Josué Daniel Vázquez Becerra (Queen's)
Second order freeness, Hadamard matrices, and signed permutation matrices.
In this talk, we first show how to calculate the joint distribution of the entries of a uniformly distributed signed permutation matrix. Then, we explore the idea of using Hadamard matrices and uniformly distributed signed permutation matrices to deliver asymptotic freeness of second order.
Thursday, February 11, 10:00 - 11:30, Jeff 222
Yinzheng Gu (Queen's)
Bi-free Independence, II
Free independence is an analogue of classical independence where tensor products are replaced by free products. The parallel between the two theories run quite deep and extends to both the analytic and combinatorial approaches to independence. Recently a model was found where free and tensor independence can co-exist on the same space. Moreover other notions of independence make sense in this model. This is a continuation from January 21.
Thursday, February 4, 10:00 - 11:30, Jeff 222
Quanyuan Chen (School of Information and Engineering, Jingdezhen Ceramic Institute)
Generalized derivations on CSL subalgebras of von Neumann algebras
We extend existing results that study when Jordan derivations are derivations. Under a mild condition, it is shown that a Jordan $(α,β)$-derivation on a CSL subalgebra of a von Neumann algebra is an $(α,β)$-derivation. It is shown that a Jordan $(α,α)$-derivation on a CSL subalgebra of a von Neumann algebra is an $(α,α)$-derivation, where $α,β$y are automorphisms on a CSL subalgebra of a von Neumann algebra. We also investigate the generalized $n$-th power maps on CSL subalgebras of von Neumann algebras.
Thursday, January 28, 10:00 - 11:30, Jeff 222
Mario Diaz (Queen's)
On the Symmetries of Multiantenna Channels
We will review some of the results given in a previous talk. Then we will discuss recent developments and further applications.
Thursday, January 21, 10:00 - 11:30, Jeff 222
Yinzheng Gu (Queen's)
Bi-free Independence
Free independence is an analogue of classical independence where tensor products are replaced by free products. The parallel between the two theories run quite deep and extends to both the analytic and combinatorial approaches to independence. Recently a model was found where free and tensor independence can co-exist on the same space. Moreover other notions of independence make sense in this model. I will review some of my recent results and indicate where further progress might be made.

Previous Schedules

Getting to Jeffery Hall from the Hotel Belvedere