This award provides support to defray expenses of US participants (primarily junior mathematicians) to attend two workshops (February 14 - 25 and April 11-21) of the Bialgebras in Free Probability program at the Schroedinger Institute in Vienna in 2011.
Free probability is a highly noncommutative probability theory with models in operator algebras, random matrices and combinatorics. The program will benefit from a large spectrum of experts (from operator algebras, combinatorics, random matrices, classical probability and mathematical physics) to examine the various sides of recent developments in free probability with a special emphasis on the recent occurrence of several kinds of bialgebra structures at a fundamental level in the subject. The first workshop period will be devoted to combinatorial, bialgebra and analytic aspects, while the second workshop period will be mostly about the operator algebra, random matrix and applications to mathematical physics aspects of the subject.
The award provides potential for great cross-fertilization between these areas of mathematics and at the same time a very good opportunity for young mathematicians (starting with graduate students and postdocs) with research interests in these areas.
Free probability is a highly noncommutative probability theory which has important connections with several other fields: operator algebras, random matrices, combinatorics and classical probability theory. Via the connection with random matrices, free probability theory has had applications to certain models in physics and to certain models of multiuser telecommunication systems. Young mathematicians who study free probability, usually start in one of the related fields of mathematics and it is important for their professional development that they have the opportunity to participate in conferences where they can meet researchers who approach free probability from different backgrounds. The project provided travel support for young mathematicians (mostly graduate students and postdocs) to participate in the program "Bialgebras in Free Probability" at the Erwin Schroedinger Institute in Vienna in the Spring of 2011. Residual funds were used one year later for travel support of young mathematicians to the workshop "Free Probability and the Large N Limit III" at UC Berkeley and also for two of the young mathematicians to travel to UC Berkeley later and give seminar talks about their work. The following young mathematicians : Natasha Blitvic (graduate student MIT), Stephen Curran (postdoc UCLA), Michael Hartglass (graduate student UCB), Weihua Liu (graduate student UCB), Adam Merberg (graduate student UCB), Gabriel Tucci (recent Ph D, researcher Bell Labs), John D. Williams (graduate student Indiana U. Bloomington) were supported for travel and acommodation to participate in the Vienna program. The more advanced among the young mathematicians (Blitvic, Curran, Tucci, Williams) gave talks at the workshops. The program included lecture series providing introductions to the topics of the workshops, an introductory course on free probability and many lectures at the workshops by experts about recent advances. The young mathematicians who received travel and accommodation support to participate in the UC Berkeley workshop are : Steven Avsec (graduate student UIUC), Natasha Blitvic (graduate student UCLA), Stephen Curran (postdoc UCLA), Benjamin Hayes (graduate student UCLA), Tod Kemp (Assistant Professor UCSD), Gabriel Tucci (recent Ph D, researcher Bell Labs), John D. Williams (postdoc Texas A&M). Several young mathematician who have received support from this grant gave laectures at the workshop: Avsec, Blitvic, Curran, Hartglass, Hayes, Kemp, Merberg, Tucci, Williams. Later, Natasha Blitvic and John D. Williams received support from the grant to give seminar talks at UC Berkeley about work in free probability. Details about the Vienna program are available on the web at www.math.tugraz.at/mathc/esi2011/index.html , www.esi.ac.at/activities/past.html and www.esiac.at/Reports/2011.pdf Details about the workshop at UC Berkeley are on thr web at www.math.ucla.edu/~shlyakht/styled/index.shtml
