Research Interests
Algebraic systems arising from mathematical physics like the Witt algebra, Virasoro algebra, Grassmann spaces, related Lie algebras and their representations.
Exterior algebra and questions regarding their pullback, equivalence, stability, rank, and classification.
The interplay between algebraic geometry, commutative algebra and category theory.
Awards
INSPIRE fellowship, awarded by the Dept. of Science and Technology, Govt. of India for the duration 2010-2015
Mitacs Globalink internship award, for pursuing a reseach project in University of Ottawa, Canada, for 12 weeks. (Summer 2014)
Reseach Projects
A complete
classification of all stable exterior forms is sought over both the real and complex fields. This involves finding the
orbits, stabilizers and normal forms for each case, under the action of GL(V) through pullback.
Construction of the SuperVirasoro algebra, which arises as a Z_2 gradation of the central extension of a Lie algebra of differential operators, called the Witt algebra, was studied. This algebra arises naturally from the calculations of string theory.
The unitary representation for the SuperConformal current algebra, seen as a semi-direct product of the SuperVirasoro and the SuperLoop algebras was found.
A minimal model was developed, as a variation of the class-1 Li-Rinzel model to explain the anomalously slower oscillations observed in pancreatic cells. The numerical integration software XPPaut was employed for solving the differential equations involved and generating the bifurcation diagrams needed.
The model was able to reproduce all experimental data on the reaction of these cells to CPA, oleate and EGTA with surprising accuracy and, is currently being written up for publication with Dr. Goel, in collaboration with Dr. Arthur Sherman and Dr. Les Satin.
The literature on
existing models of the glutathione cycle was studied and the equations were successfully simplified, making them more
tractable for any future work on this system.
Academic Course Projects
Using the concept of mollifiers, their convolution, its derivative, and their convergence, along with the stability of the initial-value-problem with regards to uniform convergence; a proof of the theorem was written up and finally presented as a chalk-and-board talk.
This was a month-long reading project at TIFR - Centre for Applicable Mathematics, Bangalore under the guidance of Dr. K. Sandeep.
The notion of
exterior forms and their pullback was studied. These concepts were then used to study a proof of Darboux theorem, and to
understand the orbits of k-forms under the action of GL(V). Certain properties of the determinant function and skew-
symmetric matrices were obtained as corollaries.
Teaching Experience
Teaching Assistant to Dr. Sriram Balasubramaniyam for Calculus II (Spring 2014)
Teaching Assistant to Dr. Asok Kumar Nanda for Real Analyis and Calculus I (Fall 2013)
Talks
On the Pulback of Exterior Forms, University of Ottawa (June 2014). This was a chalk-and board talk.
A Math Student's Apology, IISER K (February 2014). [pdf] This was a fun- presentation based loosely on G. H. Hardy's famous essay A Mathematician's Apology.
Understanding Infinity, IISER K (September 2013). This was a chalk-and board talk.
The Icons of Evolution, IISER K, in a team of 5 members, (August 2010). [pdf]
Quizmaster for IISER K's first Maths Quiz Contest (March 2013). Click here to try your hand at some of the questions.
Event organiser of the largest event, called C.S.I. in IISER K's science fest Inquivesta (March 2011).
An active member of the IISER K Dramatics club, having conceptualised, scripted, acted in and directed over a dozen plays.
Elected treasurer of IISER K's Dramatics club (2013-2014).
Other interests include English fiction, philosophy, mythology, sketching and blogging.
Playing with a Rubik's cube. Fastest time: 90 second.
Armed with a razor and clippers, trying out a variety of hair- and beard- styles.
For learning how NOT to spell my name, click here.