# Rahul Pandharipande

**Rahul Pandharipande** (born 1969) is a mathematician who is currently a professor of mathematics at the Swiss Federal Institute of Technology Zürich (ETH) working in algebraic geometry. His particular interests
concern moduli spaces, enumerative invariants associated to moduli spaces, such as Gromov–Witten invariants and Donaldson–Thomas invariants, and the cohomology of the moduli space of curves.[1][2] His father Vijay Raghunath Pandharipande was a renowned theoretical physicist who worked in the area of nuclear physics.

Rahul Pandharipande | |
---|---|

Born | 1969 (age 49–50) Amravati, Maharashtra, India |

Nationality | Portuguese |

Alma mater | Princeton University Harvard University |

Awards | Clay Research Award (2013) Infosys Prize (2013) |

Scientific career | |

Fields | Mathematics |

Institutions | ETH Zurich Princeton University Caltech University of Chicago |

Doctoral advisor | Joe Harris |

Doctoral students | Aaron Pixton |

## Educational and professional history

He received his A.B. from Princeton University in 1990 and his Ph.D. from Harvard University in 1994 with a thesis entitled `*A Compactification over the Moduli Space of Stable Curves of the Universal Moduli Space of Slope-Semistable Vector Bundles'*. His thesis advisor at Harvard was Joe Harris. After teaching at the University of Chicago and the California Institute of Technology, he joined the faculty as Professor of Mathematics at Princeton University in 2002. In 2011, he accepted a Professorship at ETH Zürich.

## Selected Publications[3]

- William Fulton and Rahul Pandharipande, Notes on stable maps and quantum cohomology, in Proceedings of Algebraic Geometry – Santa Cruz (1995), Proc. Sympos. Pure Math. 62, 45–96. (One of the standard sources on Gromov–Witten theory.)
- Tom Graber and Rahul Pandharipande, Localization of virtual classes, Inventiones Mathematicae
**135**(1999), no. 2, 487–518. (This introduced an Atiyah-Bott type localisation formula for the virtual fundamental class.) - Carel Faber and Rahul Pandharipande, Hodge integrals and Gromov–Witten theory, Inventiones Mathematicae
**139**(2000), no. 1, 173–199. - Andrei Okounkov and Rahul Pandharipande, Gromov–Witten theory, Hurwitz numbers, and completed cycles, Annals of Mathematics
**163**(2006), 517–560. - Andrei Okounkov and Rahul Pandharipande, The equivariant Gromov-Witten theory of , Annals of Mathematics
**163**(2006), 561–605. - Davesh Maulik, Nikita Nekrasov, Andrei Okounkov, and Rahul Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory I, Compositio Mathematica
**142**(2006), 1263–1285. (In this paper a change of variables is introduced to relate Gromov–Witten theory to Donaldson–Thomas theory. This work was explicitly mentioned in the citations for his 2013 Infosys Prize[2] and 2013 Clay Research Award.)[1] - Rahul Pandharipande and Richard P. Thomas, Curve counting via stable pairs in the derived category, Inventiones Mathematicae
**178**(2009), 407–447. (Here a novel set of enumerative invariants (`Pandharipande-Thomas invariants' was introduced and linked to Gromov-Witten theory and Donaldson-Thomas theory.) - Andrei Okounkov and Rahul Pandharipande, Quantum cohomology of the Hilbert scheme of points of the plane, Inventiones Mathematicae
**179**(2010), 523–557. - Rahul Pandharipande and Richard P. Thomas, The Katz–Klemm–Vafa conjecture for K3 surfaces, Forum of Mathematics, Pi
**4**(2016), e4, 111 pp. MR3508473 - Pandharipande, Rahul; Pixton, Aaron; Zvonkine, Dimitri (2015), "Relations on via 3-spin structures",
*Journal of the American Mathematical Society*,**28**(1): 279–309, doi:10.1090/S0894-0347-2014-00808-0, MR 3264769 - Janda, Felix; Pandharipande, Rahul; Pixton, Aaron; Zvonkine, Dimitri (2017), "Double ramification cycles on the moduli spaces of curves",
*Publications Mathématiques de l'IHÉS*,**125**: 221–266, arXiv:1602.04705, doi:10.1007/s10240-017-0088-x, MR 3668650 - Pandharipande, Rahul; Pixton, Aaron (2017), "Gromov–Witten/Pairs correspondence for the quintic 3-fold",
*Journal of the American Mathematical Society*,**30**(2): 389–449, arXiv:1206.5490, doi:10.1090/jams/858, MR 3600040

## Quotations

`Going into the subject [Gromov-Witten theory] and not working with the virtual fundamental class is like going to Vegas and not gambling.'[4]

## References

- "Rahul Pandharipande". Clay Mathematics Institute. Retrieved 14 March 2018.
- "Infosys Prize - Laureates - Mathematical Sciences, 2013 Prof. Rahul Pandharipande". Infosys Science Foundation. Retrieved 14 March 2018.
- CV
- http://videodl.msri.org/data/000/030/452/original/2-Pandharipande.mp4, 6:55