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Hirotaka Irie

2011-09-21
11:00:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

We develop a general framework to study Stokes phenomena of the k x k isomonodromy systems with an arbitrary Poincar\'e index r, especially which correspond to two kinds of physically interesting critical points of the multi-cut two-matrix models. Investigation of this system is important for the purpose of figuring out the non-critical version of M theory which unifies various solvable string theories in two-dimension. We start with general theorems on the profile of dominant exponents and its relation to Stokes matrices. The physical boundary conditions are then formulated as a connection to the multi-cut two-matrix models, which enables us to obtain explicit expressions of the Stokes multipliers for quite wide class of k and r. We also discuss an interesting connection between the physical boundary conditions and the discrete Hirota dynamics (T-systems) of quantum integrable systems.