IISER MOHALI

Research Area

Differential Algebra, Galois theory of differential equations

Research Interests

Just as classical Galois theory addresses polynomial equations, differential Galois theory addresses linear homogeneous differential equations. The Galois groups that arise in this context happen to be linear algebraic groups. There is also a Galois correspondence in this context that works similarly to the Galois theory of polynomial equations. The nature of the solutions of a differential equation can be analyzed by studying the differential Galois group. For instance, all the solutions of a linear homogeneous differential equation are Liouvillian, that is, the solutions can be algebraically expressed by a combination of arbitrary antiderivatives, exponentials and algebraic elements if and only if the identity component of the differential Galois group is solvable. One can also apply differential Galois theory to determine whether or not an elementary function has an elementary integral.

My current research interests:  Extend Rosenlicht's theorem on integration in finite terms to various special functions, study nonlinear differential equations and their singularities from an algebraic view-point,   understand structural properties of  noncommutative differential rings, such as central simple algebras, using techniques from differential Galois theory.