
My
main interests lie in commutative algebra, the
study of commutative rings and modules over them.
I am currently working on understanding a new
construction of Gorenstein rings called the
connected sum. I am also studying various aspects of
fibre products of rings and establishing
connections of fibre products with connectedness
theorems and exploring their links to the theory
of Gorenstein liaison.
In my earlier work, one project
involved approximating Artinian rings by
Gorenstein rings using the notion of Gorenstein
colength. Part of the work dealt with studying
bounds on this number and the other involved
constructing Gorenstein Artin rings. Techniques
used include studying inverse systems, maps from
the injective hull of the residue field to the
ring, the HoskinDeligne formula, the strong
Lefschetz property and fiber products and
connected sums of Gorenstein Artin local rings.
Another problem I have worked on dealt with
multiplicities and minimal reductions of the
maximal ideal in a local ring. Part of the work was to
understand when the maximal ideal is 3standard,
using tools from the world of positive
characteristic and applying the technique of
reducing to prime characteristic.
§ Research Summary
§ Publications

