Selected Papers and Preprints
| Based Linear Maps to the Flag Variety, a postcard authored with Balazs Elek |
 Mathematical Research Postcards
|
| The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds, with Stephen Pietromonaco and an appendix with Mike Roth. |
arXiv:2405.04701
|
| Counting Invariant Curves: A Theory of Gopakumar-Vafa Invariants for Calabi-Yau threefolds with an Involution, with Stephen Pietromonaco. |
arXiv:2203.12077
|
| Paper by my PhD student Stephen Pietromonaco: G-invariant Hilbert Schemes on Abelian Surfaces and Enumerative Geometry of the Orbifold Kummer Surface |
arXiv:2011.14020
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| G-fixed Hilbert schemes on K3 surfaces, modular forms, and eta products, with Adam Gyenge. |
arXiv:1907.01535
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| Paper by my PhD student, Nina Morishige: Genus zero Gopakumar-Vafa invariants of the Banana manifold. |
arXiv:1909.01540 |
| The Donaldson-Thomas partition function of the banana manifold. Appendix with Stephen Pietromonaco. |
arXiv:1902.08695 |
| Master's thesis of Stephen Pietromonaco: An introduction to modern enumerative geometry with applications to the banana manifold. |
arXiv:1905.07085
|
| CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms. With Georg Oberdieck. |
arXiv:1811.06102 |
| Locally Maximally Entangled States of Multipart Quantum Systems. With Samuel Leutheusser, Zinovy Reichstein, and Mark Van Raamsdonk |
arXiv:1801.03508 |
| Existence of Locally Maximally Entangled States via Geometric Invariant Theory. With Zinovy Reichstein and Mark Van Raamsdonk |
Journal link.
arXiv:1708.01645 |
| Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex. With Martijn Kool |
arXiv:1608.07369 |
| Trace identities for the topological vertex. With Martijn Kool and Ben Young |
Journal link.
arXiv:1603.05271 |
| Master's thesis of Leo Hsu: Formal-local Structure of the Hilbert Scheme of Points on Three-Dimensional Complex Affine Space around Special Monomial Ideals |
UBC Link.
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| Curve counting on abelian surfaces and threefolds. With Georg Oberdieck, Rahul Pandharipande, and Yin Qizheng |
arXiv:1506.00841 |
| Donaldson-Thomas theory of K3xE via the topological vertex. |
arXiv:1504.02920 |
| Curve counting invariants for crepant resolutions. With David Steinberg. |
arXiv:1208.0884 |
| Motivic Classes of Commuting Varieties via Power Structures. With Andrew Morrison. |
arXiv:1206.5864 |
| The Orbifold Topological Vertex. With Chuck Cadman and Ben Young. |
arXiv:1008.4205 |
| Motivic degree zero Donaldson-Thomas invariants. With Kai Behrend and Balazs Szendroi. |
arXiv:0909.5088 |
| BPS invariants for resolutions of polyhedral singularities. With Amin Gholampour. |
arXiv:0905.0537 |
| Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds. appendix to a paper by Ben Young. |
arXiv:0802.3948 |
| The Quantum McKay Correspondence for Polyhedral Singularities. With Amin Gholampour. |
arXiv:0803.3766 |
| Hurwitz-Hodge integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture. With Amin Gholampour. |
arXiv:0708.4244 |
| Roots systems and the quantum cohomology of ADE resolutions. With Amin Gholampour. |
arXiv:0707.1337 |
| The Crepant Resolution Conjecture. With Tom Graber. |
TEX
DVI
math.AG/0610129 |
| Super-rigid Donaldson-Thomas invariants. With Kai Behrend. |
math.AG/0601203 |
| The Orbifold Quantum Cohomology of C^2/Z_3 and Hurwitz-Hodge integrals. With Tom Graber and Rahul Pandharipande. |
math.AG/0510335 |
| The local Gromov-Witten theory of curves. With Rahul Pandharipande. |
math.AG/0411037 |
| On the rigidity of stable maps to Calabi-Yau
threefolds. With Rahul Pandharipande. |
math.AG/0405204 |
| The closed topological vertex via the Cremona
transform. With Dagan Karp. |
math.AG/0311208 |
| Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory. With Rahul Pandharipande. |
math.AG/0306316 |
| Surface bundles over surfaces of small genus.
With Ron Donagi. Published
in "Geometry and Topology" |
math.AG/0105203 |
| Surface bundles: some interesting examples. With Ron
Donagi and Andras Stipsicz. |
|
| BPS states of curves in Calabi-Yau 3-folds. With
Rahul Pandharipande. Published
in "Geometry and Topology" |
math.AG/0009025 |
| 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) |
|
| Evidence for a conjecture of Pandharipande |
math.AG/0008036 |
| Multiple covers and the integrality conjecture for
rational curves in Calabi-Yau threefolds. With Sheldon Katz and
Conan Leung. |
math.AG/9911056 |
| G-Bundles on Abelian
surfaces, Hyperkahler manifolds and Stringy Hodge numbers. With Ron
Donagi and Conan Leung. |
math.AG/0004159 |
| Counting curves on Irrational surfaces. With
Conan Leung. | |
| Generating functions for the number of curves
on Abelian surfaces. With Conan Leung. |
math.AG/9802125 |
| The enumerative geometry of K3 surfaces and
modular forms. With Conan Leung. | alg-geom/9711031 |
| Orbifold Euler characteristics and the number of
commuting n-tuples in symmetric groups. With Jason
Fulman. | math.CO/9712248 |
| Seiberg-Witten Theory and Z/2^p actions
on spin 4-manifolds | dg-ga/9704010 |
| Seiberg-Witten a la Furuta and genus bounds for
classes with divisibility | |
| Instantons on S^4 and
\bar{CP^2}, rank stabilization, and Bott periodicity.
With Marc Sanders. | alg-geom/9612008 |
| The Rank Stable Topology of Instantons on
\bar{CP^2}. With Marc Sanders. | alg-geom/9610008 |
| The multi-monopole equations for Kahler
surfaces. With Richard Wentworth. |
|
| The relative Donaldson invariants of \bar{CP^2} |
|