Priyavrat Deshpande's webpage

Welcome to my homepage!

I am an assistant professor at the Chennai Mathematical Institute. I 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.

Mathematics

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.

My thesis, titled "Arrangements of Submanifolds and the Tangent Bundle Complement", has been published by the Scholarship@Western and is available for download here.

Seminars

I and Ronno Das ran a weekly seminar on configuration spaces with a focus on understanding their cohomology as representations of the symmetric group. The seminar page is here.

Student supervision

  1. K. Chandrashekhar (2013-14): Supervised a year long project on some problems in enumerative combinatorics.
  2. R. Das (2014-15):  Supervised M.Sc. thesis titled Salvetti complex construction for manifold reflection arrangements.
  3. A. Ray (2014-15): Project - Topology of the complement of affine plane curves.
  4. A. Khetan (2015-16): Supervised M.Sc. thesis titled A cellular model for the configuration space of points on graphs (pdf).
  5. N. Adhikari (2016-17): Supervised M.Sc. thesis titled Discrete Morse theory on moduli spaces of planar polygons (pdf).

Published papers

  1. On a generalization of Zaslavsky's theorem for hyperplane arrangements,
    (Annals of Combinatorics, 18(1):35-55, 2014). arXiv
  2. Deletion-restriction in toric arrangements, with K. Sutar, (J. Ramanujan Math. Soc. 31(1):17-30, 2016) arXiv.(JRMS)
  3. Arrangements of spheres and projective spaces, to appear in Rocky Mountain J. Math 46(5): 1447-1487, 2016, link, arXiv.
  4. 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, arXiv.
  5. 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

Available online

Accepted for publication

  1. Face enumeration for line arrangements in a 2-torus, with K. Chandrashekhar arXiv. (accepted for publication in IJPAM)

Preprints/ In preparation

  1. Arrangements of submanifolds and the tangent bundle complement, arXiv.
  2. Topological aspects of reflection arrangements in spheres, with R. Das.
  3. Salvetti-type diagram models for tangent bundle complements.
top

Teaching

Present

August-Nov 2017: Introduction to Manifolds

Past courses

Jan-Apr 2017
Graduate Topology 2
Aug-Nov 2016
Combinatorics 1
Aug-Nov 2015
Homotopy theory
Jan-April 2015
Differential topology (reading course)
Jan-April 2015
Topics in topology
Aug-Nov 2014
Algebraic topology
May 2014
Differential topology (A.F.S.)
Jan-April 2014
Algebraic topology II
Aug-Nov 2013
Algebraic topology
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 Northeastern)
Fall 2011 Math 1231: Calculus for Business and Economics. (at Northeastern)
Fall 2011 Math 1341: Calculus and Science and Engineering. (at Northeastern)

© 2016 Priyavrat Deshpande
Template design by Andreas Viklund | Icons from Iconza.com