Wednesday March 29, 2017 11:00 A125
Čestmír Burdík (Czech Technical University in Prague) Algebraic Bethe ansatz Abstract: On the example of gl(2) we will show the formulation of algebraic Bethe ansatz. The generalization to nested Bethe ansatz for the gl(3) case will be done. Finally some new results will be mentioned. |
Tuesday April 4, 2017 11:00 C101
Andrey Krutov (Institute of Mathematics, Polish Academy of Sciences) Lie algebroids over infinite jet spaces (Joint work with A.V. Kiselev) Abstract: We define Lie algebroids over infinite jet spaces. The example of such construction is given by Hamiltonian operators and Lie algebra-valued zero-curvature representations for partial differential equations. The talk is based on the following papers: (1) A.V. Kiselev, J.W. van de Leur, Variational Lie algebroids and homological evolutionary vector fields, Theor. Math. Phys. 167 (2011), N3, 772-784; arXiv:1006.4227 [math.DG]. (2) A.V. Kiselev, A.O. Krutov, Non-Abelian Lie algebroids over jet spaces, J. Nonlin. Math. Phys. 21 (2014), N2, 188-213; arXiv:1305.4598 [math.DG]. |
Thursday April 6, 2017 11:00 A125
Andrey Krutov (Institute of Mathematics, Polish Academy of Sciences) Gardner's deformations of integrable systems (Joint work with A.V. Kiselev) Abstract: By tracking the relations between zero-curvature representations (ZCR) and Gardner's deformations, we construct the solution of the deformation problem for the N=2, a=4-SKdV equation. We show that the ZCR found by Das et al. yields a system of new nonlocal variables such that their derivatives contain the Gardner deformation for the classical KdV equation. In turn, from this system of nonlocalities we derive Gardner's deformation for N=2 supersymmetric a=4 Korteweg-de Vries equation. Likewise we obtain Gardner's deformation for the Krasil'shchik-Kersten system from a zero-curvature representation found for it by Karasu-Kalkanli et al. |
Friday April 7, 2017 14:00 C101
Andrey Krutov (Institute of Mathematics, Polish Academy of Sciences) On gradings modulo 2 of simple Lie algebras in characteristic 2 (Joint work with A. Lebedev) Abstract: In characteristic 2, the classification of modulo 2 gradings of simple Lie algebras is vital for the classification of simple finite dimensional Lie superalgebras: with each grading a simple Lie superalgebra is associated, see arXiv:1407.1695 (S. Bouarroudj, A. Lebedev, D. Leites, and I. Shchepochkina, "Restricted Lie (super)algebras, classification of simple Lie superalgebras in characteristic 2"). No classification of gradings was known for any type of simple Lie algebras, bar restricted Zassenhaus algebras (a.k.a. Witt algebras, i.e., Lie algebras of vector fields with truncated polynomials as coefficients) on not less than 3 indeterminates. Here we completely describe gradings modulo 2 for several series of simple Lie algebras: special linear, two inequivalent orthogonal, and projectivizations of their derived, except for psl(4) for which a conjecture is given. All of the corresponding superizations are known, but a corollary proves non-triviality of a deformation of a simple Lie superalgebra (new result). For nonrestricted Zassenhaus algebras on one indeterminate, there are more types of modulo 2 gradings than for the restricted Zassenhaus algebras, and several corresponding simple Lie superalgebras seem to be new. This is proved for small values of the height of divided powers; the general answer is conjectural. |
Wednesday April 12, 2017 11:00 A125
Radosław Kycia (Krakow University of Technology and Masaryk University, Brno) Singularities, self-similar solutions and their generalizations Abstract: I will present our recent results on self-similar solutions of semilinear wave equations, their generalizations and related problems involving (movable and fixed) singularities of differential equations. Bibliography: [1] R. Kycia, G. Filipuk, On the generalized Emden-Fowler and isothermal spheres equations. [2] R. Kycia, G. Filipuk, On the singularities of the Emden-Fowler type equations. [3] R. Kycia, On similarity in the evolution of semilinear wave and Klein-Gordon equations: Numerical surveys. [4] R. Kycia, On self-similar solutions of semilinear wave equations in higher space dimensions. |
TBA (June 12, 2017?)
Matěj Tušek (Czech Technical University in Prague) TBA |
TBA (Fall 2017?)
Urs Schreiber (Institute of Mathematics, Czech Academy of Sciences) TBA |
TBA (Fall 2017?)
Arman Taghavi-Chabert (University of Torino) TBA |
2017 2016 |