It will also explain the existence of many identities that appeared in Ramanujan's Notebooks. Work has been done in solving several hard problems in homotopy theory, such as classification of self smash products and loop suspensions, by using representation theory. Various relations among these different areas have been established. The research is attacking celebrated problems in homotopy theory, representation theory and low dimensional topology, such as the homotopy groups of spheres, the Barratt conjecture and the Kervaire invariant conjecture, with possible applications in mathematical physics. The main focus is recursion theory on weak fragments of Peano arithmetic, which is also called reverse recursion theory.
Blocks having small non-Abelian defect group are also of interest.
The research involves topics in number theory and arithmetic geometry, such as elliptic curves and modular curves, as well as their applications in cryptography, coding theory, combinatorial designs and sequences. It has applications in disciplines ranging from the physical sciences to biology and medicine to economics and finance. The probability group is interested in both basic and applied research in the field and has done work in Poisson approximation, Stein's method, self-similar processes, martingales, Brownian motion, inequalities and limit theorems.