

Seminar on analytic theory of differential equations
June 3, 2015 14:00–15:30, Moscow, Steklov Mathematical Institute, Room 440 (8 Gubkina)






Knot invariants and Oainleve equations

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Abstract:
On the conference "Knots and Links in Fluid Flows" in IUM at one talk the following result was formulated. A HOMFLY invariant of a toric knot $(n,n+1)$ can be expressed through variables that describe a discrete dynamical system. Recurrent relations for these variables porvide that the generating function of these variables satisfy the Painlvev 2 equation.
I am going to tell about invariants of knots that come from fourdimensiona manifolds. Actually the invariants of manifolds can be organized into formal solutions of PDE. In particulat I'll explain how to a symplectic fourdimensional manifold there corresponds a solution of WDVV. And among reductions of these equations there are Painleve and Kdf equations

