Research
Research
Wavelets
Classification of integrable pdes
The idea behind the classification of integrable pdes is to use the representation theory of affine Lie algebras to define the classification. This is possible because the fundamental modules of the affine Lie algebras are integrable and so are also modules for the action of an associated group. The action of the group on the highest weight vector defines the tau-functions which are fundamental in the theory of integrable equations. The tau-function satisfy Hirota equations which can also be obtained from the representation theory. A brief introduction to this approach is given in: Integrable equations and affine Lie algebras.
MOND and alternative theories of gravitation/ Loop quantum gravity
The Hirota equations associated with simply laced affine Lie algebras: the cuspidal class , J. Math. Phys., 55, 021703 (2014).