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## Periodic and rapid decay rank two self-adjoint commuting differential operators

Title: Periodic and rapid decay rank two self-adjoint commuting differential operators

Speaker: Andrey Mironov (Sobolev Institute of Mathematics, Novosibirk and Novosibirsk State University, Russia)

AbstractSelf-adjoint commuting ordinary differential operators of rank two are considered. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g + 2 is self-adjoint. An equation on potentials $V (x),W(x)$ of the self-adjoint operator $L_4 = (\partial_x^2 + V(x))^2+W(x)$ and some additional data is introduced. With the help of this equation operators with polynomial, periodic and rapid decay coefficients are constructed. Some problems related to rank two solutions of soliton equations are discussed.

Time: 4:00-5:00 pm; May 27; 2013

Place: Conference Room A304, Department of Mathematical Sciences

Profile of speaker: Dr. Andrey Mironov’s main research interests are integrable systems and geometry. His series results obtained jointly with P.G. Grinevich and S.P. Novikov was included into the “List of best results of the Russian Academy of Sciences” in 2010. He was also an invited speaker of the European Math. Congress in Krakow in 2012.

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