Event
Marco Bertola, Universit茅 Concordia
Tuesday, March 14, 2017 15:30to16:30
Room 4336, Pavillon Andr茅-Aisenstadt, 2920, Chemin de la tour, 5th floor, Montreal, QC, H3T 1J4, CA
The Malgrange form and Fredholm determinants
We consider the classical factorization problem of matrix symbols depending analytically on parameters on a closed contour (i.e. a Riemann--Hilbert problem). We show how to define a function $ au$ which is locally analytic on the space of deformations and that is expressed as a Fredholm determinant of an operator of ``integrable'' type in the sense of Its-Izergin-Korepin-Slavnov. The construction is not unique and the non-uniqueness highlights the fact that the tau function is really the section of a line bundle.