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This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover.
Toward an enumerative geometry of the moduli space of curves
David Mumford · 1983
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The moment map and equivariant cohomology
Michael Atiyah and Raoul Bott · 1984
Earlier work this paper cites.
Representation Theory
William Fulton and Joe Harris · 1991
Earlier work this paper cites.
Transitive factorisations into transpositions and holomorphic mappings on the sphere
I. P. Goulden and D. M. Jackson · 1997
Earlier work this paper cites.
Moduli of Curves
Joe Harris and Ian Morrison · 1998
Earlier work this paper cites.
Localization of virtual classes
T. Graber and R. Pandharipande · 1999
Earlier work this paper cites.
Hurwitz numbers and intersections on moduli spaces of curves
Torsten Ekedahl, Sergei Lando, Michael Shapiro, and Alek Vainshtein · 2001
Earlier work this paper cites.
On the tautological ring of M ¯ g , n \overline{M}_{g,n}
Tom Graber and Ravi Vakil · 2001
Earlier work this paper cites.
Notes on psi classes
Joachim Kock · 2001
Earlier work this paper cites.
Stable maps and branch divisors
B. Fantechi and R. Pandharipande · 2002
Earlier work this paper cites.
Towards the geometry of double Hurwitz numbers
Ian Goulden, David M. Jackson, and Ravi Vakil · 2003
Earlier work this paper cites.
Hodge integrals, Hurwitz numbers, and virtual localization
Tom Graber and Ravi Vakil · 2003
Earlier work this paper cites.
Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
Tom Graber and Ravi Vakil · 2003
Earlier work this paper cites.
Mirror Symmetry
Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, and Eric Zaslow · 2003
Cited alongside, same era.
Frobenius algebras and 2 2 D topological quantum field theories
Joachim Kock · 2003
Cited alongside, same era.
A short proof of the λ g \lambda_{g} -conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
Ian Goulden, David Jackson, and Ravi Vakil · 2006
Cited alongside, same era.
Changes of variables in ELSV-type formulas
Sergey Shadrin and Dimitri Zvonkine · 2007
Cited alongside, same era.
Chamber behavior of double Hurwitz numbers in genus 0
S. Shadrin, M. Shapiro, and A. Vainshtein · 2008
Cited alongside, same era.
The moduli space of curves and Gromov-Witten theory
R. Vakil · 2008
Cited alongside, same era.
Abelian Hurwitz-Hodge integrals
P. Johnson, R. Pandharipande, and H.-H. Tseng · 2011
Later among the works it cites.
The tropicalization of the moduli space of curves
Dan Abramovich, Lucia Caporaso, and Sam Payne · 2012
Later among the works it cites.
Hurwitz numbers, ribbon graphs, and tropicalization
Paul Johnson · 2012
Later among the works it cites.
Stable maps to rational curves and the relative jacobian
Steffen Marcus and Jonathan Wise · 2013
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Gonality of algebraic curves and graphs
Lucia Caporaso · 2014
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A geometric perspective on the polynomiality of double Hurwitz numbers
Renzo Cavalieri and Steffen Marcus · 2014
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KP hierarchy for Hodge integrals
M. Kazarian · 2009
Cited alongside, same era.
Gromov-Witten theory, Hurwitz numbers, and matrix models
A. Okounkov and R. Pandharipande · 2009
Cited alongside, same era.
On the structure of Goulden-Jackson-Vakil formula
S. Shadrin · 2009
Cited alongside, same era.
Tropical Hurwitz numbers
Renzo Cavalieri, Paul Johnson, and Hannah Markwig · 2010
Cited alongside, same era.
Tropical open Hurwitz numbers
B. Bertrand, B. Brugallé, and G. Mikhalkin · 2011
Cited alongside, same era.
Wall crossings for double Hurwitz numbers
Renzo Cavalieri, Paul Johnson, and Hannah Markwig · 2011
Cited alongside, same era.
Tropical compactification and the Gromov–Witten theory of ℙ 1 \mathbb{P}^{1}
Renzo Cavalieri, Hannah Markwig, and Dhruv Ranganathan · 2014
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Tropicalizing the space of admissible covers
Renzo Cavalieri, Hannah Markwig, and Dhruv Ranganathan · 2014
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Double total ramifications for curves of genus 2
Nicola Tarasca · 2014
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Cycles on the moduli space of curves, 2015
Rahul Pandharipande · 2015
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Relations on M ¯ g , n \overline{M}_{g,n} via 3 3 -spin structures
Rahul Pandharipande, Aaron Pixton, and Dimitri Zvonkine · 2015
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A first course in Hurwitz Theory
Renzo Cavalieri and Eric Miles · 2016
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Double ramification cycles on the moduli spaces of curves
Felix Janda, Rahul Pandharipande, Aaron Pixton, and Dimitri Zvonkine · 2016
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