Names: Prof JC Ndogmo
Position: Associate Professor
Qualification(s):
- PhD in Mathematics (Univ of Montreal)
- DEA (Strasbourg)
- BSc (Univ of Ydé)
Research areas of specialization: Lie algebras, Lie group analysis of Differential equations. Also, Financial Maths and a little bit of Data Science.
Contact details (Tel.No, Email(s), and Office no):
- Tel: 015 962 8904
- Email:Jean-claude.ndogmo @univen.ac.za
Description: Part of my current research interests is focused on the study of symmetry integrable systems, and more specifically on the identification, classification and generation of such systems. A by-product of this study is an attempt to characterize the very powerful recursion operators which can indeed generate integrable systems but remain largely unexplored and challenging to find. Recently, in order to formally extend to PDEs the notion of iterative equations known only for ODEs, we introduced a new method of group classification termed the method of indeterminates, as another alternative to the intricate problem of group classification.
The initial aim of our extension of the notion of iterative equations to PDEs was to generalize to this much broader type of equations the wealth of results we achieved for systems of ODEs, of any type most often, and in particular of any order and dimension. We also discovered that the symmetry group approach offers a unique way to generate the sought after soliton solutions of nonlinear wave equations, under certain symmetry operators and this topic now also forms part of our research interests. We are however also interested in the study of these
solitons through the Hirota and the Darboux transformation methods, and in particular through an in-depth leveraging of the properties of Lax pairs.
In our study of Lie algebras the focus is generally on invariant functions of the adjoint or the co-adjoint representations, and in particular on Casimir operators, due to the role they play in physics, in representation theory, and in other mathematically based fields. We’ve thus exhibited several types of Lie algebras admitting a fundamental set of invariants consisting of Casimir Operators, including for instance Lie algebras with a nilpotent radical, and given amongst several other simple results a characterization of solvable Lie algebras that do not
possess any nontrivial invariant function. Naturally some of our results usually apply to abstract Lie algebras themselves. This includes some structure theorems we formulated based of Kravchuk signature, and which are widely applied to the classification of Lie algebras, as well as a determination of the maximal dimension of the center of solvable Lie algebras, amongst several other results.
