priyavrat deshpande

Chennai Mathematical Institute
SIPCOT IT park,Siruseri, TN 603103
+91 (044)6748 0962;
pdeshpande AT cmi DOT ac DOT in

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.

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 the 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.

Research

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.

I am recipient of SERB's MATRICS grant for the period of 3 years (June 2018 - March 2021).

Activities

  • I and Dheeraj Kulkarni organized a 3-day meeting (July 16-18, 2018) for graduate students and postdocs interested in various aspects of topology. The details can be found here.
  • I co-organized Computational Geometry Day at CMI on 25/01/2018. For more information click here.
  • 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.

Publications

  1. Face enumeration for line arrangements in a 2-torus,
    with K. Chandrashekhar, Indian J. Pure Appl. Math., 48(3), 2017.arXiv.
  2. On arrangements of pseudohyperplanes,
    Proc. Indian Acad. Sci. (Math. Sci.) Vol. 126, No. 3, 2016, pp. 399–420.
  3. Coxeter transformation groups and reflection arrangements in smooth manifolds,
    with R. Das, J. Homot. Rel. Struct.,11:571-597, 2016, arXiv.
  4. Arrangements of spheres and projective spaces,
    Rocky Mountain J. Math 46(5): 1447-1487, 2016, link, arXiv.
  5. Deletion-restriction in toric arrangements,
    with K. Sutar, J. Ramanujan Math. Soc. 31(1):17-30, 2016. arXiv.
  6. On a generalization of Zaslavsky's theorem for hyperplane arrangements,
    Annals of Combinatorics, 18 (1):35-55, 2014. arXiv
Preprints/ In preparation
  1. The Goresky-MacPherson formula for toric arrangements . arXiv
  2. Arrangements of submanifolds and the tangent bundle complement, arXiv.

  3. Topological aspects of reflection arrangements in spheres, with R. Das.

  4. Salvetti-type diagram models for tangent bundle complements.


teaching

This semester I am teaching Graduate Topology 2

Past courses

  1. Aug-Nov 2018 Topological Robotics.
  2. Aug-Nov 2018 Intro to Manifolds.
  3. Jan-Apr 2018 Topics in combinatorics .
  4. Aug-Nov 2017 Intro to Manifolds
  5. Jan-Apr 2017 Graduate Topology 2
  6. Aug-Nov 2016 Combinatorics 1
  7. Aug-Nov 2015 Homotopy theory
  8. Jan-Apr 2015 Differential topology
  9. Jan-Apr 2015 Topics in topology
  10. Aug-Nov 2014 Algebraic topology
  11. Jan-Apr 2014 Algebraic topology II
  12. Aug-Nov 2013 Algebraic topology
  13. Jan-Apr 2013 Intro to reflection groups.
  14. Aug-Nov 2012 Real analysis

supervision

Postdoc
  1. Anurag Singh (2018-): PhD (2018) from IIT Kanpur.
PhD students
  1. N. Daundkar (2017-)
MSc students
  1. Naageswaran M. (2018-19):
  2. N. Adhikari (2016-17): Discrete Morse theory on moduli spaces of planar polygons (thesis).
  3. A. Khetan (2015-16): A cellular model for the configuration space of points on graphs (thesis).
  4. R. Das (2014-15): Salvetti complex construction for manifold reflection arrangements (thesis).
  5. Karthik C. (2013-14): Face numbers of toric arrangements.

Misc.