## 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.

## 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 (present): Supervising M.Sc. thesis on
topological robotics.

#### 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

Jan-Apr 2017: Graduate Topology
2

#### Past courses

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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