Research

Selected papers & preprints

A chronological collection of research papers and preprints, with arXiv, journal, and archival links.

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48items, listed newest first

2026
Based Maps to Lagrangian Grassmannians, Quivers, and Bott Periodicity, with Ravi Vakil.
Preprint (2026).
arXiv:2607.10956
2026
The Motivic Class of the Space of Genus Zero Maps to the Flag Variety, with Balazs Elek, Freddie Manners, George Salafatinos, and Ravi Vakil.
Preprint (2026).
arXiv:2601.07222
2025
Based Linear Maps to the Flag Variety, a postcard authored with Balazs Elek
Mathematical Research Postcards 2 (2025), no. 2.
Journal PDF
2025
The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds, with Stephen Pietromonaco and an appendix with Mike Roth.
Communications in Number Theory and Physics 19 (2025), no. 3, 527–571.
Journal arXiv:2405.04701
2024
Counting Invariant Curves: A Theory of Gopakumar-Vafa Invariants for Calabi-Yau threefolds with an Involution, with Stephen Pietromonaco.
Algebraic Geometry 11 (2024), no. 2, 256–289.
Journal arXiv:2203.12077
2022
G-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products, with Adam Gyenge.
Épijournal de Géométrie Algébrique 6 (2022), article 6.
Journal arXiv:1907.01535
2021
The Donaldson-Thomas partition function of the banana manifold. Appendix with Stephen Pietromonaco.
Algebraic Geometry 8 (2021), no. 2, 133–170.
Journal arXiv:1902.08695
2020
CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms. With Georg Oberdieck.
Communications in Number Theory and Physics 14 (2020), no. 4, 785–862.
Journal arXiv:1811.06102
2019
Locally Maximally Entangled States of Multipart Quantum Systems. With Samuel Leutheusser, Zinovy Reichstein, and Mark Van Raamsdonk
Quantum 3 (2019), article 115.
Journal arXiv:1801.03508
2019
Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex. With Martijn Kool
Forum of Mathematics, Sigma 7 (2019), e7, 45 pp.
Journal arXiv:1608.07369
2018
Existence of Locally Maximally Entangled States via Geometric Invariant Theory. With Zinovy Reichstein and Mark Van Raamsdonk
Annales Henri Poincaré 19 (2018), no. 8, 2491–2511.
Journal arXiv:1708.01645
2018
Trace identities for the topological vertex. With Martijn Kool and Ben Young
Selecta Mathematica 24 (2018), no. 2, 1527–1548.
Journal arXiv:1603.05271
2018
Curve counting on abelian surfaces and threefolds. With Georg Oberdieck, Rahul Pandharipande, and Yin Qizheng
Algebraic Geometry 5 (2018), no. 4, 398–463.
Journal arXiv:1506.00841
2018
Donaldson-Thomas theory of $K3 \times E$ via the topological vertex.
In Geometry of Moduli, Abel Symposia 14 (2018), 35–64, Springer.
Journal arXiv:1504.02920
2016
Curve counting invariants for crepant resolutions. With David Steinberg.
Transactions of the American Mathematical Society 368 (2016), no. 3, 1583–1619.
Journal arXiv:1208.0884
2015
Motivic Classes of Commuting Varieties via Power Structures. With Andrew Morrison.
Journal of Algebraic Geometry 24 (2015), no. 1, 183–199.
Journal arXiv:1206.5864
2013
Motivic degree zero Donaldson-Thomas invariants. With Kai Behrend and Balazs Szendroi.
Inventiones Mathematicae 192 (2013), no. 1, 111–160.
Journal arXiv:0909.5088
2012
The Orbifold Topological Vertex. With Chuck Cadman and Ben Young.
Advances in Mathematics 229 (2012), no. 1, 531–595.
Journal arXiv:1008.4205
2010
Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds. appendix to a paper by Ben Young.
Duke Mathematical Journal 152 (2010), no. 1, 115–153.
Journal arXiv:0802.3948
2009
BPS invariants for resolutions of polyhedral singularities. With Amin Gholampour.
Selecta Mathematica 15 (2009), no. 4, 521–533.
Journal arXiv:0905.0537
2009
The Quantum McKay Correspondence for Polyhedral Singularities. With Amin Gholampour.
Inventiones Mathematicae 178 (2009), no. 3, 655–681.
Journal arXiv:0803.3766
2009
Hurwitz-Hodge integrals, the $E_6$ and $D_4$ root systems, and the Crepant Resolution Conjecture. With Amin Gholampour.
Advances in Mathematics 221 (2009), no. 4, 1047–1068.
Journal arXiv:0708.4244
2009
The Crepant Resolution Conjecture. With Tom Graber.
In Algebraic Geometry—Seattle 2005, Proc. Sympos. Pure Math. 80 (2009), 23–42.
Journal arXiv:math/0610129
2008
Roots systems and the quantum cohomology of ADE resolutions. With Amin Gholampour.
Algebra & Number Theory 2 (2008), no. 4, 369–390.
Journal arXiv:0707.1337
2008
The Orbifold Quantum Cohomology of $\mathbb{C}^2/\mathbb{Z}_3$ and Hurwitz-Hodge integrals. With Tom Graber and Rahul Pandharipande.
Journal of Algebraic Geometry 17 (2008), no. 1, 1–28.
Journal arXiv:math/0510335
2008
The local Gromov-Witten theory of curves. With Rahul Pandharipande.
Journal of the American Mathematical Society 21 (2008), no. 1, 101–136.
Journal arXiv:math/0411037
2007
Super-rigid Donaldson-Thomas invariants. With Kai Behrend.
Mathematical Research Letters 14 (2007), no. 4, 559–571.
Journal arXiv:math/0601203
2006
On the rigidity of stable maps to Calabi-Yau threefolds. With Rahul Pandharipande.
Geometry & Topology Monographs 8 (2006), 97–104.
Journal arXiv:math/0405204
2005
The closed topological vertex via the Cremona transform. With Dagan Karp.
Journal of Algebraic Geometry 14 (2005), 529–542.
Journal arXiv:math/0311208
2005
Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory. With Rahul Pandharipande.
Duke Mathematical Journal 126 (2005), no. 2, 369–396.
Journal arXiv:math/0306316
2002
Surface bundles over surfaces of small genus. With Ron Donagi.
Geometry & Topology 6 (2002), 59–67.
Journal arXiv:math/0105203
2002
Evidence for a conjecture of Pandharipande
Turkish Journal of Mathematics 26 (2002), no. 1, 69–73.
Journal arXiv:math/0008036
2001
Surface bundles: some interesting examples. With Ron Donagi and Andras Stipsicz.
Turkish Journal of Mathematics 25 (2001), no. 1, 61–68.
Journal PDF
2001
BPS states of curves in Calabi-Yau 3-folds. With Rahul Pandharipande.
Geometry & Topology 5 (2001), 287–318.
Journal arXiv:math/0009025
2001
Multiple cover formulas for Gromov-Witten invariants and BPS states (for the Proceedings of the conference ``Algebraic Geometry and Integrable Systems Related to String Theory" in RIMS, June 2000)
Sūrikaisekikenkyūsho Kōkyūroku 1232 (2001), 144–159.
Journal PDF
2001
Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds. With Sheldon Katz and Conan Leung.
Journal of Algebraic Geometry 10 (2001), no. 3, 549–568.
Journal arXiv:math/9911056
2001
$G$ -Bundles on Abelian surfaces, Hyperkähler manifolds and Stringy Hodge numbers. With Ron Donagi and Conan Leung.
Turkish Journal of Mathematics 25 (2001), no. 1, 195–236.
Journal arXiv:math/0004159
2000
The enumerative geometry of $K3$ surfaces and modular forms. With Conan Leung.
Journal of the American Mathematical Society 13 (2000), no. 2, 371–410.
Journal arXiv:alg-geom/9711031
2000
Instantons on $S^4$ and $\overline{\mathbb{CP}}{}^2$ , rank stabilization, and Bott periodicity. With Marc Sanders.
Topology 39 (2000), no. 2, 331–352.
Journal arXiv:alg-geom/9612008
1999
Counting curves on Irrational surfaces. With Conan Leung.
Surveys in Differential Geometry 5 (1999), 313–339.
Journal PDF
1999
Generating functions for the number of curves on Abelian surfaces. With Conan Leung.
Duke Mathematical Journal 99 (1999), no. 2, 311–328.
Journal arXiv:math/9802125
1998
Orbifold Euler characteristics and the number of commuting n -tuples in symmetric groups. With Jason Fulman.
Annals of Combinatorics 2 (1998), no. 1, 1–6.
Journal arXiv:math/9712248
1998
Seiberg-Witten Theory and $\mathbb{Z}/2^p$ actions on spin 4-manifolds
Mathematical Research Letters 5 (1998), nos. 1–2, 165–183.
Journal arXiv:dg-ga/9704010
1997
Seiberg-Witten a la Furuta and genus bounds for classes with divisibility
Turkish Journal of Mathematics 21 (1997), no. 1, 55–59.
Journal PDF
1997
The Rank Stable Topology of Instantons on $\overline{\mathbb{CP}}{}^2$ . With Marc Sanders.
Proceedings of the American Mathematical Society 125 (1997), no. 12, 3763–3768.
Journal arXiv:alg-geom/9610008
1997
The relative Donaldson invariants of $\overline{\mathbb{CP}}{}^2$
Forum Mathematicum 9 (1997), no. 3, 325–366.
Journal PDF
1996
The multi-monopole equations for Kahler surfaces. With Richard Wentworth.
Turkish Journal of Mathematics 20 (1996), no. 1, 119–128.
Journal PDF
1994
Texture Bestiary: From Symmetry-Breaking Patterns to Topological Field Configurations. With Sean M. Carroll and Ted Pyne.
Physical Review D 50 (1994), no. 4, 2806–2818.
Journal arXiv:hep-ph/9312254

Selected papers & preprints

Based Maps to Lagrangian Grassmannians, Quivers, and Bott Periodicity, with Ravi Vakil.

The Motivic Class of the Space of Genus Zero Maps to the Flag Variety, with Balazs Elek, Freddie Manners, George Salafatinos, and Ravi Vakil.

Based Linear Maps to the Flag Variety, a postcard authored with Balazs Elek

The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds, with Stephen Pietromonaco and an appendix with Mike Roth.

Counting Invariant Curves: A Theory of Gopakumar-Vafa Invariants for Calabi-Yau threefolds with an Involution, with Stephen Pietromonaco.

G-fixed Hilbert schemes on K3K3K3 surfaces, modular forms, and eta products, with Adam Gyenge.

The Donaldson-Thomas partition function of the banana manifold. Appendix with Stephen Pietromonaco.

CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms. With Georg Oberdieck.

Locally Maximally Entangled States of Multipart Quantum Systems. With Samuel Leutheusser, Zinovy Reichstein, and Mark Van Raamsdonk

Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex. With Martijn Kool

Existence of Locally Maximally Entangled States via Geometric Invariant Theory. With Zinovy Reichstein and Mark Van Raamsdonk

Trace identities for the topological vertex. With Martijn Kool and Ben Young

Curve counting on abelian surfaces and threefolds. With Georg Oberdieck, Rahul Pandharipande, and Yin Qizheng

Donaldson-Thomas theory of K3×EK3 \times EK3×E via the topological vertex.

Curve counting invariants for crepant resolutions. With David Steinberg.

Motivic Classes of Commuting Varieties via Power Structures. With Andrew Morrison.

Motivic degree zero Donaldson-Thomas invariants. With Kai Behrend and Balazs Szendroi.

The Orbifold Topological Vertex. With Chuck Cadman and Ben Young.

Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds. appendix to a paper by Ben Young.

BPS invariants for resolutions of polyhedral singularities. With Amin Gholampour.

The Quantum McKay Correspondence for Polyhedral Singularities. With Amin Gholampour.

Hurwitz-Hodge integrals, the E6E_6E6​ and D4D_4D4​ root systems, and the Crepant Resolution Conjecture. With Amin Gholampour.

The Crepant Resolution Conjecture. With Tom Graber.

Roots systems and the quantum cohomology of ADE resolutions. With Amin Gholampour.

The Orbifold Quantum Cohomology of C2/Z3\mathbb{C}^2/\mathbb{Z}_3C2/Z3​ and Hurwitz-Hodge integrals. With Tom Graber and Rahul Pandharipande.

The local Gromov-Witten theory of curves. With Rahul Pandharipande.

Super-rigid Donaldson-Thomas invariants. With Kai Behrend.

On the rigidity of stable maps to Calabi-Yau threefolds. With Rahul Pandharipande.

The closed topological vertex via the Cremona transform. With Dagan Karp.

Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory. With Rahul Pandharipande.

Surface bundles over surfaces of small genus. With Ron Donagi.

Evidence for a conjecture of Pandharipande

Surface bundles: some interesting examples. With Ron Donagi and Andras Stipsicz.

BPS states of curves in Calabi-Yau 3-folds. With Rahul Pandharipande.

Multiple cover formulas for Gromov-Witten invariants and BPS states (for the Proceedings of the conference ``Algebraic Geometry and Integrable Systems Related to String Theory" in RIMS, June 2000)

Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds. With Sheldon Katz and Conan Leung.

GGG-Bundles on Abelian surfaces, Hyperkähler manifolds and Stringy Hodge numbers. With Ron Donagi and Conan Leung.

The enumerative geometry of K3K3K3 surfaces and modular forms. With Conan Leung.

Instantons on S4S^4S4 and CP‾2\overline{\mathbb{CP}}{}^2CP2, rank stabilization, and Bott periodicity. With Marc Sanders.

Counting curves on Irrational surfaces. With Conan Leung.

Generating functions for the number of curves on Abelian surfaces. With Conan Leung.

Orbifold Euler characteristics and the number of commuting n -tuples in symmetric groups. With Jason Fulman.

Seiberg-Witten Theory and Z/2p\mathbb{Z}/2^pZ/2p actions on spin 4-manifolds

Seiberg-Witten a la Furuta and genus bounds for classes with divisibility

The Rank Stable Topology of Instantons on CP‾2\overline{\mathbb{CP}}{}^2CP2. With Marc Sanders.

The relative Donaldson invariants of CP‾2\overline{\mathbb{CP}}{}^2CP2

The multi-monopole equations for Kahler surfaces. With Richard Wentworth.

Texture Bestiary: From Symmetry-Breaking Patterns to Topological Field Configurations. With Sean M. Carroll and Ted Pyne.

G-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products, with Adam Gyenge.

Donaldson-Thomas theory of $K3 \times E$ via the topological vertex.

Hurwitz-Hodge integrals, the $E_6$ and $D_4$ root systems, and the Crepant Resolution Conjecture. With Amin Gholampour.

The Orbifold Quantum Cohomology of $\mathbb{C}^2/\mathbb{Z}_3$ and Hurwitz-Hodge integrals. With Tom Graber and Rahul Pandharipande.

$G$ -Bundles on Abelian surfaces, Hyperkähler manifolds and Stringy Hodge numbers. With Ron Donagi and Conan Leung.

The enumerative geometry of $K3$ surfaces and modular forms. With Conan Leung.

Instantons on $S^4$ and $\overline{\mathbb{CP}}{}^2$ , rank stabilization, and Bott periodicity. With Marc Sanders.

Seiberg-Witten Theory and $\mathbb{Z}/2^p$ actions on spin 4-manifolds

The Rank Stable Topology of Instantons on $\overline{\mathbb{CP}}{}^2$ . With Marc Sanders.

The relative Donaldson invariants of $\overline{\mathbb{CP}}{}^2$