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

**报告题目****:** eriodic and rapid decay rank two self-adjoint commuting differential operators

**报告人****:** Andrey Mironov (Sobolev Institute of Mathematics, Novosibirk and Novosibirsk

State University, Russia)

**时间****: **** **2013年5月27日（星期一）16:00-17:00

**地点****: **** **理科楼数学系A304

**摘要：**Self-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.

**报告人简介：**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.

**联系人：**马辉