## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, January 17, 2014 — 3:30 PM EST

One of the most basic problems of free probability is how to calculate the moments of a sum of two free elements in a noncommutative probability space. This is solved by using the R-transforms of the elements in question. Among the possible approaches to the R-transform of an element x, the very first one that was found (Voiculescu, 1986) goes by replacing x with a ”canonical operator” X which has the same moments as x, and where X is written in terms of the shift operator on l2. This approach extends to the case of a d-tuple of elements x1, ..., xd – the given d-tuple is replaced by a d-tuple of canonical operators X1,...,Xd, with the Xi’s written in terms of left-creation operators on the full Fock space F over Cd.

In 2013, Voiculescu introduced the concept of bi-freeness for elements in a noncommutative probability space; this calls for studying (2d)-tuples of canonical operators X1, ..., Xd, Y1, ..., Yd, where X1, ..., Xd are acting on the left and Y1, ..., Yd are acting on the right, on the same full Fock space F as above. In this talk I will present a recent joint work done with Mitja Mastnak (arXiv:1312.0269), where we study such (2d)-tuples of canonical operators.

Location

MC - Mathematics & Computer Building

5136B

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1