HOẠT ĐỘNG TRONG TUẦN

Địa điểm: P6, Nhà A14, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội
Tóm tắt: We discuss an algebraic problem which arises from the study of the nonlinear Schrodinger equation (NLS for brevity). This problem is about separation and irreducibility (over the ring of integers) of  the characteristic polynomials of the graphs, describing blocks of a normal form for the NLS. For the cubic NLS the problem has been completely solved  (see [ C.Procesi, M. Procesi and B.Van Nguyen, The energy graph of the nonlinear Schrodinger equation, Rend. Lincei. Mat. Appl., 24(2), 2013, p.229-301]), meanwhile for higher degree NLS it is still open, even in small dimensions (see [C.Procesi, The energy graph of the nonlinear Schrodinger equation, open problems, Int.J. Algebra Comput., 23(4), 2013, p. 943-962] ). In this talk the author will present the analysis origin of the problem and give a partial answer for this problem, in particular, the author will prove Separation and Irreducibility Conjecture for NLS of arbitrary degree on 1-dimensional and 2-dimensional tori.