Research Interests
I am interested in: Subfactor Theory, Hopf Algebras, Quantum invariants, Commutative Algebra and Algebraic
Geometry.
List of publications
- Homological invariants of powers of an ideal
Proceedings of the American Mathematical Society, Vol 118, P. 757-764,
1993.
- Integrally closed modules over two-dimensional regular local rings
Transactions of the American Mathematical Society, Vol 347, P. 3551-3573,
1995.
- Symmetric powers of a complete module over a two-dimensional
regular local ring, with D. Katz
Transactions of the American Mathematical Society, Vol 349, P. 747-762,
1997.
-
Asymptotic behaviour of Castelnuovo-Mumford regularity
Proceedings of the American Mathematical Society, Vol 128, P. 407-411,
2000.
- The subgroup subfactor, with V. S. Sunder
Mathematica Scandinavica, Vol 86, P. 45-74, 2000.
- The algebra of G-relations, with R. Srinivasan and V. S.
Sunder
Proceedings of the Indian Academy of Sciences, Vol 110, No 3, P. 263-292,
2000.
- Flatness and fusion coefficients, with V. S. Sunder
Pacific Journal of Mathematics, Vol 201, P. 177 - 204, 2001.
- Spectra of principal graphs, with V. S. Sunder
International Journal of Mathematics, Vol 12, No 2, P. 203-210, 2001.
- Topological quantum field theories from subfactors, with V.
S. Sunder
CRC Research Notes in Mathematics Series, 423, 2000.
- The planar algebra associated to a Kac algebra, with V. S.
Sunder and Zeph Landau
Proceedings of the Indian Academy of Sciences, Vol
113, P.15-51, 2003.
- Hilbert functions of points on Schubert varieties in the
Grassmannian, with K. N. Raghavan
Journal of Algebra, Vol 270, No 1,
P. 28-54, 2003.
- On Jones' planar algebras, with V. S. Sunder
Journal of Knot Theory and its Ramifications, Vol 13, No.2, P.219-248, 2004.
- Planar algebras and the Ocneanu-Szymanski theorem, with
Paramita Das
Proceedings of the American Mathematical
Society, Vol 133, P. 2751-2759, 2005.
- Complete invariants of complex semisimple Hopf algebras,
with Sumanth Datt and V. S. Sunder
Mathematics Research
Letters, Vol 10, P.571-586, 2003.
- A complete set of numerical invariants for a subfactor,
with V. S. Sunder
Journal of Functional Analysis, Vol 212, No 1,
P.1-27, 2004.
-
Bounds on the a-invariant and reduction numbers of ideals ,
with Clare D'Cruz and J. K. Verma
Journal of Algebra, Vol 274, No 2,
P.594-601, 2004.
- Picture invariants
and the isomorphism problem for complex semisimple Lie algebras ,
with K. N. Raghavan
Contemporary Mathematics, Vol 390, P.127-136, 2005.
- The planar algebra of a semisimple and cosemisimple Hopf algebra
with V. S. Sunder
Proceedings of the Indian Academy of Sciences,
Vol 116, P. 443-458, 2006.
- Subfactors and 1+1 dimensional TQFTs
with Vishwambhar Pati and V. S. Sunder
International Journal of Mathematics,
Vol 18, No. 1, P. 69-112, 2007.
- Planar algebras and Kuperberg's 3-manifold invariant
with V. S. Sunder
Journal of Operator Theory, To appear.
- Temperley-Leib and non-crossing partition planar algebras
with V. S. Sunder
Contemporary Mathematics, To appear.
- Alternating matrices over commutative rings
with T. Y. Lam and R. Swan
Contemporary Mathematics, To appear.