## 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

- 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).
- N.
Adhikari (2016-17): Supervised M.Sc. thesis titled
Discrete Morse theory on moduli spaces of planar
polygons (pdf).

#### Published papers

- On a generalization of Zaslavsky's theorem for
hyperplane arrangements,

(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,
arXiv.

- 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

- 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.

### 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

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