Welcome to my homepage!
I am an assistant professor at the Chennai Mathematical
completed my PhD in 2011 in mathematics from University of
Western Ontario, Canada under the supervision of Graham
Denham and Ján Mináč. Then I spent a year at Northeastern
in Boston followed by three years as a post-doc here at
CMI. My mathematical interests broadly include Algebraic
topology and Combinatorics. In particular I am interested
in the theory of arrangements (hyperplanes, tori,
submanifolds etc.), topological robotics and applications
of algebraic topology. A copy of my (slightly old) research statement.
I am one of the placement coordinators at CMI. If you
are looking for hiring mathematicians to work in finance,
machine learning, formal verification etc. feel free to
write to me. Visit our placement page here.
I am also local coordinator for the Madhava
Mathematics Competition. If you are from around
Chennai and are interested in participating in this
competition then get in touch.
My research involves combinatorial and topological
understanding of hyperplane arrangements. In my PhD thesis
I initiated a study of submanifold arrangements. In
particular I am interested in spherical, projective and
toric arrangements. My current projects include an
investigation of discrete subgroups of diffeomorphisms
that are generated by certain involutions, a
generalization of Artin groups, enumerative aspects of
collection of geodesics on compact surfaces and topology
of certain algebraic varieties.
- K. Chandrashekhar (2013-14): Supervised a year long project on some problems in enumerative combinatorics.
- R. Das (2014-15): Supervised M.Sc. thesis titled Salvetti complex construction for manifold reflection arrangements.
- A. Ray (2014-15): Project - Topology of the complement of affine plane curves.
- A. Khetan (2015-16): Supervised M.Sc. thesis titled A cellular model for the configuration space of points on graphs (pdf).
Adhikari (2016-17): Supervised M.Sc. thesis titled
Discrete Morse theory on moduli spaces of planar
- On a generalization of Zaslavsky's theorem for
(Annals of Combinatorics, 18(1):35-55, 2014). arXiv
- Deletion-restriction in toric arrangements, with K. Sutar, (J. Ramanujan Math. Soc. 31(1):17-30, 2016) arXiv.(JRMS)
- Arrangements of spheres and projective spaces, to appear in Rocky Mountain J. Math 46(5): 1447-1487, 2016, link, arXiv.
- Coxeter transformation groups and reflection
arrangements in smooth manifolds, with R. Das,
J. Homot. Rel. Struct.,11:571-597 (2016), DOI 10.1007/s40062-015-0117-8,
- On arrangements of pseudohyperplanes, Proc. Indian
Acad. Sci. (Math. Sci.) Vol. 126, No. 3, August 2016,
pp. 399–420. DOI 10.1007/s12044-016-0286-3
Accepted for publication
- Face enumeration for line arrangements in a
2-torus, with K. Chandrashekhar arXiv.
(accepted for publication in IJPAM)
Preprints/ In preparation
- Arrangements of submanifolds and the tangent bundle complement, arXiv.
- Topological aspects of reflection arrangements in
spheres, with R. Das.
- Salvetti-type diagram models for tangent bundle complements.
August-Nov 2017: Introduction to
||Differential topology (reading course)
||Differential topology (A.F.S.)
||Algebraic topology II
|Jan - Apr 2013||Introduction to reflection groups.|
|Dec. 2012||Differential topology (A.F.S.)
|Aug-Nov 2012||Real analysis (graduate course)
|Spring 2012||Math 1231: Calculus for Business and Economics. (at
|Fall 2011||Math 1231: Calculus for Business and Economics. (at Northeastern)|
|Fall 2011||Math 1341: Calculus and Science and Engineering. (at Northeastern)|