10103 Category Theory, K Theory, Homological Algebra
10102 Algebraic and Differential Geometry
Partial Differential EquationsCondensed Matter PhysicsDifferential GeometryMathematical PhysicsString Theory
Index theory, noncommutative geometry, elliptic genera
Citation at year of election
Mathai Varghese is a major contributor to the field of geometric analysis. He is justly famous for several seminal articles, including what is known in the literature as the Mathai-Quillen formalism in topological field theories; L2-invariants for covering spaces; the hyperbolic space and noncommutative geometry model of the fractional quantum Hall effect; projective Atiyah-Singer index theory; twisted K-theory and T-duality in String theory which is popularly known as the ‘Theory of Everything’. In lay-person’s terms, he has proved a number of important results that involve the geometry and topology of manifolds, familiar examples in low dimensions are curves and surfaces.