Rahul Pandharipande
Department of Mathematics
ETH Zürich
My papers can be found on the
arXiv.
Most recent papers are
linked below.
Beginning students might benefit
from these more
introductory writings.
Two papers on localization and Hodge integrals:
I.
Localization of virtual classes
(with T. Graber)
II.
Hodge integrals and Gromov-Witten theory (with C. Faber)
Papers on tautological classes:
I.
Constructions of non-tautological classes
(with T. Graber)
II.
Relative maps and tautological classes (with C. Faber)
III.
New topological recursion relations (with X. Liu)
IV.
Tautological and non-tautological cohomology (with C. Faber)
V.
CohFTs with non-tautological classes (with D. Zvonkine and
Appendix by D. Petersen)
VI.
Zero cycles on the moduli space of curves (with J. Schmitt)
VII.
λg, 0-sections, and the log Chow ring of the moduli of curves
(with S. Molcho and J. Schmitt)
VIII.
Log tautological rings
(with D. Ranganathan, J. Schmitt, and P. Spelier)
Gromov-Witten theory, Hurwitz
numbers, and matrix models (with A. Okounkov)
A Fock space approach to Severi
degrees (with Y. Cooper)
A trilogy (with A. Okounkov) on the Gromov-Witten theory of target curves:
I, II, III
The papers fully determine the Gromov-Witten theory of target curves.
A
calculator has been written by J. Bryan.
Gromov-Witten theory of complete intersections
(with H. Argüz, P. Bousseau, and D. Zvonkine)
Conjectures
equating the Gromov-Witten theory of 3-folds with the holomorphic Chern-Simons
theory of
Donaldson-Thomas (with D.
Maulik, N. Nekrasov, and
A. Okounkov): I, II
Results related to the local theories of curves:
I. Local Gromov-Witten theory (with J. Bryan)
II. Quantum cohomology of the Hilbert scheme of points of the plane (with A. Okounkov)
III. Local Donaldson-Thomas theory (with A. Okounkov)
IV. QDE of the Hilbert scheme of points of the plane (with A. Okounkov)
V. Higher
genus Gromov-Witten theory of the Hilbert scheme of points of the plane (with H.-H. Tseng)
VI.
Descendents
and Fourier-Mukai (with H.-H. Tseng)
Gromov-Witten/Donaldson-Thomas correspondence
for toric 3-folds (with D. Maulik, A. Oblomkov, and A. Okounkov)
GW/PT descendent correspondence
via
vertex operators
(with A. Oblomkov and A. Okounkov)
Virasoro constraints
for stable pairs on toric 3-folds
(with M. Moreira, A. Oblomkov, and A. Okounkov)
A topological view of Gromov-Witten theory (with D. Maulik)
New calculations in Gromov-Witten theory (with D.
Maulik)
Gromov-Witten theory and Noether-Lefschetz theory
(with D. Maulik)
Noether-Lefschetz theory and the Yau-Zaslow
conjecture (with A. Klemm, D. Maulik, and E. Scheidegger)
Curves on K3 surfaces
and modular forms (with D. Maulik and R. Thomas)
Katz-Klemm-Vafa conjecture for K3 surfaces
(with R. Thomas)
Motivic stable pairs invariants for
K3 surfaces
(with S. Katz and A. Klemm)
Curve counting on
K3xE, Igusa cusp forms, and descendent integration
(with G. Oberdieck)
Curve counting on
abelian varieties
(with J. Bryan, G. Oberdieck, and Q. Yin)
Curve counting via stable
pairs in the derived category
(with R. Thomas)
The 3-fold
vertex via stable pairs
(with R. Thomas)
Stable pairs and
BPS invariants
(with R. Thomas)
13/2 ways of counting curves (with R. Thomas)
Descendents for stable pairs on local curves:
rationality
(with A. Pixton)
Descendents for stable pairs on local curves:
stationary theory
(with A. Pixton)
Descendents for stable pairs on
toric 3-folds
(with A. Pixton)
Gromov-Witten/Pairs descendent
correspondence for toric varieties
(with A. Pixton)
Gromov-Witten/Pairs correspondence
for the
quintic Calabi-Yau
(with A. Pixton)
Descendents for stable pairs on 3-folds
Descendent correspondence for families
Counting disks on the quintic 3-fold
(with J. Solomon and J. Walcher)
Intersection theory on the moduli of disks, KdV, and Virasoro
(with J. Solomon and R. Tessler)
Enumerative geometry of Calabi-Yau
4-folds
(with A. Klemm)
Enumerative geometry of Calabi-Yau
5-folds,
Appendix
(with A. Zinger)
Algebraic cobordism revisited
(with M. Levine)
Algebraic cobordism for bundles
on varieties
(with Y.-P. Lee)
Abelian Hurwitz-Hodge integrals (with P. Johnson
and H.-H. Tseng)
Tropical vertex group (with M. Gross
and B. Siebert)
Quivers, curves, and the tropical vertex (with M. Gross)
Moduli of stable quotients (with A. Marian
and D. Oprea)
Stable quotients and the holomorphic anomaly
equation (with H. Lho)
Holomorphic anomaly equations for the formal quintic
(with H. Lho)
Crepant resolution and the holomorphic anomaly equation for
[C3/Z3]
(with H. Lho)
Papers on tautological rings of the moduli of curves of compact type:
I, II,
revised
Related results on tautological rings of the moduli of nonsingular
curves (with A. Pixton)
Relations on the moduli space of stable curves via 3-spin
structures (with A. Pixton and D. Zvonkine)
Hypergeometric series A and B (with A. Buryak and F. Janda)
A calculus
for the moduli space of curves
Cohomological field theory calculations
Moduli of twisted canonical divisors (with G. Farkas)
Appendix on the weighted fundamental class (with
F. Janda, A. Pixton, and D. Zvonkine)
Double ramification cycles (with F. Janda, A. Pixton, and D. Zvonkine)
Double ramification cycles for target varieties (with F. Janda, A. Pixton, and D. Zvonkine)
Tautological relations via r-spin structures
(with A. Pixton and D. Zvonkine)
Appendix on the class of the locus
of holomorphic differentials (with
F. Janda, A. Pixton, and D. Zvonkine)
Universal twisted double ramification cycles (with Y. Bae, D. Holmes, J. Schmitt, and R. Schwarz)
Logarithmic double ramification cycles (with D. Holmes, S. Molcho, A. Pixton, and J. Schmitt)
Segre classes and Hilbert schemes of points (with A. Marian
and D. Oprea)
On Lehn's conjecture in rank 1 and
higher rank (with A. Marian and D. Oprea)
Relations in the tautological ring of the moduli of K3 surfaces (with Q. Yin)
The Chow ring of the moduli of K3 surfaces of degree 2 (with S. Canning and D. Oprea)
Tautological projections for cycles
on the moduli space of abelian varieties (with S. Canning, S. Molcho, and D. Oprea)
Tautological and non-tautological cycles
on the moduli space of abelian varieties (with S. Canning and D. Oprea)
Virtual Euler characteristics of Quot schemes
of surfaces (with D. Oprea)
Rationality of descendent series for
Quot schemes of surfaces (with D. Johnson and D. Oprea)
The virtual K-theory of Quot schemes of
surfaces (with N. Arbesfeld, D. Johnson, W. Lim, and D. Oprea)
Slopes of the Verlinde bundles (with A. Marian
and D. Oprea)
Chern characters of the Verlinde bundles (with A. Marian, D. Oprea, A. Pixton, and D. Zvonkine)
Tevelev degrees and Hurwitz moduli (with A. Cela
and J. Schmitt)
Enumerativity of virtual Tevelev degrees (with C. Lian)
Tevelev degrees and Gromov-Witten theory
(with A. Buch)
Irrationality of the
Hilbert scheme of points (with G. Farkas and A. Sammartano)
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