Mathematics Research Centre, Queen Mary Department of Mathematics, Brunel University

"RANDOM MATRICES AND RELATED TOPICS"

Monthly Colloquia

Date and time: 13 June 2003, 15:00 and 16:30

Location: Room M128, Department of Mathematics, Brunel University (Uxbridge)

Speaker: Alexander Orlov (Center of Nonlinear Studies, Russian Academy of Sciences) (15:00-16:00)

"Tau-functions and Matrix Integrals"

Abstract: We generalize certain known matrix integrals (Harish-Chandra-Itzukson-Zuber, Gross-Witten, etc.) using a notion of tau-function of matrix argument. We also consider asymptotic expansion of some matrix integrals in terms of tau-functions of a hypergeometric type.

Speaker: Dr. E. Kanzieper (Weizmann Institute) (16:30-17:30)

"On Exact Integrability of Replica Field Theories"

Abstract: Legitimacy of replica field theories has been a point of controvercy for over two decades. Inspired by an ongoing discussion, we critically review a so-called "replica symmetry breaking" approach, and claim exact integrability of nonlinear replica sigma models derived in the context of random matrix theories. This progress became possible due to a discovered connection between replica field theories and the theory of integrable hierarchies. Further applications of the formalism are briefly discussed.