Seminar on Free Probability and Random Matrices Fall 2018

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() ); // -->

Thursday, November 29, 4:30 - 6:00, Jeff 422
Gang-Gyun Youn (Queen's)
Some questions on Jones-Wenzl projections in view of quantum information theory
It is very natural to study separability or PPT property of quantum states in view of quantum information theory and the need to study those properties for so-called Jones-Wenzl projections has emerged in recent years. In this talk, I am going to introduce the notions of separability, PPT property and Jones-Wenzl projections.
Thursday, October 18, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
Right Hilbert A-modules, part 2
For the last talk, we gave some motivating examples and the definition of right A-module. We will begin this talk by showing some properties of  A-valued pre inner product, and then we will deduce the process to construct a right Hilbert A-module. Next, we will introduce the operators on  right Hilbert A-modules, and proving some properties of the corresponding adjoint operators.
Thursday, October 11, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
Right Hilbert A-modules
Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case..
Thursday, October 4, 4:30 - 6:00, Jeff 422
Pei-Lun Tseng (Queen's)
$A$-Valued Theory
In order to study operator-valued probability, we need some basic knowledge of C*-algebras. In this talk, I am trying to review what is a C*-algebra.  and some properties of C*-algebras. The GNS construction will be covered, which is known as the follows: every C*-algebras can be represented as a algebra of bounded linear operators on a Hilbert space. This construction gives us good starting point to study matrices over a C*-algebra. If time permits, I will introduce right Hilbert $A$-modules.
Thursday, September 27, 4:30 - 6:00, Jeff 422
Jamie Mingo (Queen's)
Operator Values Freeness and Non-commutative functions, II