Within Kerala School of Mathematics, we have the following loosely defined research groups:
Non-Commutative Functional Analysis.
Non-commutative functional analysis in general and quantum aspects such as approximation and convexity in the context of operator spaces and operator systems in C*-algebras is an active research area in functional analysis at Kerala School of Mathematics.
One of the thrust areas at Kerala School of Mathematics is Analytic Number Theory. Questions regarding distribution of prime numbers and other related functions are studied in depth. Algorithms for the computation of Multiple Zeta Values to very high orders of accuracy, in both the theoretical and implementation aspects, have been an area of focused research at Kerala School of Mathematics. The relationship between multiple zeta values and multiple Apéry-like sums have very high importance in the subject.
The field of Several Complex Variables has grown enormously in multiple directions in the latter half of the previous century with the work of great mathematicians like Cartan, Oka, Kohn, Hörmander, Fefferman, Catlin and Steven Bell to name a few. It has also shown that these multiple directions of development within mathematics can eventually end up in fruitful interactions between them. The symbiotic relationships that algebra, differential geometry, partial differential equations, algebraic geometry, and Banach algebras enjoy with Several Complex Variables have led to major developments in all of these subjects. Several Complex Variables is an active area of research at Kerala School of Mathematics.
At different stages of its development, Teichmüller theory received strong impetuses from Complex analysis, geometry, and algebraic topology. It had a major impact on other fields, including low-dimensional topology, algebraic topology, hyperbolic geometry, geometric group theory, representations of discrete groups in Lie groups, symplectic geometry, theoretical physics to name a few. It also established important connections between some of the aforementioned sub-fields. Teichmüller Theory is one of the major thrust areas in Kerala School of Mathematics.