Event
Marco Bertola, Université Concordia
Tuesday, March 14, 2017 15:30to16:30
Room 4336, Pavillon André-Aisenstadt, CA, QC, Montreal, 2920, Chemin de la tour, 5th floor, 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.