Quantum Probabilistic Symmetries

• David Evans, Martin Lindsay, Gilles Pisier, Dan Voiculescu

• Rolf Gohm, John Gough, Claus Köstler

The topic of this London Mathematical Society (LMS) regional meeting and workshop is located at the crossroad of several modern mathematical disciplines which have seen spectacular progress in the past decades: operator algebras, representations of large groups, noncommutative probability and quantum information. The aim is to present recent progress in these areas to a wide mathematical audience to foster further research projects on the interplay of the above listed topics.

Symmetries in a quantum setting are explored along many different approaches, based on groups, quantum groups, subfactors etc. A new approach to the study of such symmetries has recently been opened by the successful transfer of foundational results on distributional symmetries from classical probability to free probability and noncommutative probability. This transfer indicates all kinds of subtle interrelations between seemingly unrelated treatments of symmetries in a quantum setting.

We plan to explore new promising connections between:

• quantum symmetries in free probability
• quantum symmetries in subfactor theory and exactly solvable models
• noncommutative de Finetti theorems and central limit theorems
• representations and combinatorics of large groups (e.g. infinite symmetric or braid group)
• symmetries in quantum information theory and their applications

There will be introductory mini-courses to some of these topics.

The meeting and workshop are held at the Institute of Mathematics & Physics situated on Aberystwyth University's Penglais Campus in the Physical Sciences Building (Campus Map).

All participants are requested to register online for the workshop. It is recommended for workshop participants to arrive on the evening of Sunday, 2 September 2012.

• Begin of Workshop: Monday, 3 September 2012 at 09:00
  End of Workshop: Friday, 7 September 2012 at 15:00

The participation at the workshop is free for LMS members, research students and invited speakers. All other participants are subject to a registration fee of £80.

The meeting is embedded into the workshop.

• Opening of Meeting: Monday, 3 September 2012 at 13:45
  Closing of Meeting: Monday, 3 September 2012 at 18:30

The lectures of this meeting are aimed at a general mathematical audience. All interested, whether LMS members or not, are most welcome to attend this event. There is no fee for attending the meeting.

The LMS Midlands Regional Meeting is followed by a dinner on Monday, 3 September 2012 at 19:30. To reserve a place at the dinner, registrator online or contact the principal organiser. The cost of the dinner will be £30, including drinks.

• Claus Köstler (E-mail: )
  Institute of Mathematics and Physics
  Physical Sciences Building, Penglais Campus
  Aberystwyth University
  Aberystwyth SY23 3BZ