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 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 (April 2018 - March 2021).

Activities

  • I and Dheeraj Kulkarni are organizing 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. 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.


teaching

This semester I am teaching topics in combinatorics .

Past courses

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

supervision

  1. N. Daundkar (2017-) current PhD student.
  2. N. Adhikari (2016-17): Supervised M.Sc. thesis titled Discrete Morse theory on moduli spaces of planar polygons (thesis).
  3. A. Khetan (2015-16): Supervised M.Sc. thesis titled A cellular model for the configuration space of points on graphs (thesis).
  4. R. Das (2014-15): Supervised M.Sc. thesis titled Salvetti complex construction for manifold reflection arrangements (thesis).
  5. K. Chandrashekhar (2013-14): Supervised a year long project on some problems in enumerative combinatorics.

Misc.