ICTP Mathematics Seminars - Thursday, 18 April, starting at 14:30 (Célestin Kurujyibwami and Roman O. Popovych)

[ICTP Math Section]

Mathematics Seminars Afternoon

Venue: Luigi Stasi seminar room (ICTP Leonardo da Vinci Building)

Thursday, 18 April 2019 (14:30 - 17:30)
----------------------------------------

14:30 - 15:30 Roman O. Popovych (Faculty of Mathematics, University of 
Vienna, Austria & Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine)

Title: Computation of contractions of Lie algebras

Abstract: Limiting processes (contractions) of Lie algebras appear in 
different areas of physics and mathematics, where Lie algebras arise, 
e.g., in the study of representations, invariants and special functions. 
The algebraic counterpart of the notion of contractions of Lie algebras 
is given by degenerations of Lie algebras.

The main attention in the talk is paid to the practical computation of 
contractions of Lie algebras. We present a wide list of necessary 
conditions for the contraction existence. Particular ways for realizing 
contractions, which are relevant to physics and includes simple and 
generalized Inönü–Wigner contractions and Saletan (linear) contractions, 
are discussed and the limitation for using them is clarified. We also 
plan to present the complete description of contractions of Lie algebras 
of dimension not greater than four, of five- and six-dimensional 
nilpotent algebras and of almost Abelian Lie algebras over both the 
complex and real field.

15:30 - 16:00 break

16:00 - 17:00 Célestin Kurujyibwami (University of Rwanda, Kigali, Rwanda)

Title: Group classification of multidimensional nonlinear Schrödinger 
equations

Abstract: We describe the equivalence groupoid and the equivalence group 
of the class N of generalized multidimensional Schrödinger equations 
with variable mass and show that this class is not normalized. We then 
partition this class into two disjoint normalized subclasses and derive 
their corresponding equivalence groups. Restricting to the case of 
constant mass equal to one, we characterize the point transformations of 
the subclasses of the class N with respect to specific values of the 
arbitrary elements, in particular we do this for the class V of 
multidimensional nonlinear Schrödinger equations with potentials and 
modular nonlinearities. This class also turns out not to be normalized. 
We partition it into three normalized subclasses, and this allows us to 
apply the algebraic method and solve each subclass completely for space 
dimension two. The group classification in each involves three integers 
that are invariant with respect to the adjoint action of the equivalence 
transformations. As a result, a full list of Lie symmetry extensions 
together with their corresponding families of potentials in the class V 
is presented.

Everyone is welcome to attend


-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela