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.
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 (present): Supervising M.Sc. thesis on
- 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.
Jan-Apr 2017: Graduate Topology
||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)|