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Aparna Dar
PhD (S.U.N.Y StonyBrook, USA)
Professor, Department of Mathematics and Statistics
Research Interest
My current research interest is in the field of Knot Theory. Since Knot Theory is just about 100 years old, there are many open problems in this research area. In particular, I am interested in the study of amphicheirality, the study of closed braids, and the knot polynomials, specially the Jones polynomial.
Faculty Building,
Room Number 504.
IIT Kanpur,
Kanpur 208016.
Specialization
Differential Geometry, Algebraic Topology and Knot Theory.
Education
PhD, State University of New York at StonyBrook , U.S.A. in December 1984.Thesis Title:Intersection R-Torsion and Analytic Torsion for PseudomanifoldsThesis Supervisor: Professor Jeff Cheeger, N.Y.U, USA
Masters in Mathematics from I.I.T. Kanpur in May, 1980.
Teaching Area
Real Analysis
Topology
Differential Geometry
Algebraic Topology,
Knot Theory
Selected Publications
Intersection R-Torsion and Analytic Torsion for Pseudomanifolds, Mathematische Zeitschrift, Number 194, pages 193-216 (1987)
Intersection Whitehead Torsion and the s-cobordism theorem for Pseudomanifolds, Mathematische Zeitschrift, Number 199, pages 171-179 (1988)
Simplicial Intersection Homology Theory, Euler Characterestic and a Simplicial Lefchetz Fixed Point Theorem, Indian Journal of Mathematics, (B.N.Prasad Birth Centenary Commemoration Volume), Volume 42, No2 pages 221-231(2000)
Amphicheiral Knots with every even crossing number , Journal of Knot Theory and its Ramifications, Volume 16, Number 1, January 2007 , Pages 43-44
Examples of amphicheiral knots of braid index 3, Proceedings of the National Academy of Sciences, India, Section-A , Volume 81, Part 3, pages 221-222 (2011)
Editorial Board of the Journal “ Mathematics Student “ Published by the Indian Mathematical Society as of 12 April 2022.
Awards & Fellowships
Received Distinguished Teacher Award on Teachers Day, 5 September 2020 from the Director, I.I.T. Kanpur
Received Excellence in Teaching Award on Teachers Day, 5 September 2020 from the Director, I.I.T. Kanpur
Research Result
Solved Kirby's open problem on Knot Theory " Are there alternating amphicheiral knots of every even crossing number" with a positive, affirmative class of examples (JKTR Vol 16 2007).
Discovered new symmetries which give new classes of amphicheiral knots of braid index 3 (Proc Nat Acad Sciences,
Vol 81, 2011). Presently continuing research in the area of knot theory specially braid closures and Jones polynomials.
Extra Curricular Activities
Deeply interested in spiritual traditions , knowledge and philosophy. Am an active member
of Gayatri Pariwar, a worldwide spiritual organization, with a following of over a million
members.
Also very interested in empowerment of women and protection of the girl child. Am a member of Manushi, an Indian group for Empowerment of women and underprivileged.
Also interested in musical traditions of both east and west. Have learnt Indian classical music from Dagar family in the Dhrupad tradition.
Keywords
Knot Theory, Algebraic Topology, Differential Geometry
Professional Experience
Post Doctoral member at the Institute for Advanced Study, Princeton, New Jersey, U.S.Afrom September 1984-85
Post Doctoral visiting position at Tata Institute of Fundamental Research, (T.I.F.R), Mumbaifrom August 1985-July 1987.
Post-Doctoral visiting position at Institute of Mathematical Sciences, (MatScience), Chennaifrom January 1988- July 1988
Post-Doctoral visiting position at International Centre for Theoretical Physics (I.C.T.P),Trieste, Italy from December 1988-June 1989.
Joined as Lecturer in Mathematics at I.I.T. Kanpur in 1989 and have been employed heresince then.