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 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.

I am coorganizing Computational Geometry Dat at CMI. For more information click here.

Publications

  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.
  3. Arrangements of spheres and projective spaces,
    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, arXiv.
  5. On arrangements of pseudohyperplanes,
    Proc. Indian Acad. Sci. (Math. Sci.) Vol. 126, No. 3, 2016, pp. 399–420.
  6. Face enumeration for line arrangements in a 2-torus,
    with K. Chandrashekhar, Indian J. Pure Appl. Math., 48(3), 2017.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

student 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.