Welcome to my homepage!
I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics.
In the Fall 19 I teach a class on Topics in Enumerative Geometry.
Algebraic Geometry, in particular K3 surfaces, holomorphic-symplectic varieties, Gromov-Witten theory, Donaldson-Thomas theory.
Modular and Jacobi forms.
Phone: +49 228 73-62271
Office: Endenicher Allee 60, 1.028
Endenicher Allee 60
- Gromov-Witten invariants of the Hilbert scheme of points of a K3 surface
Geometry & Topology, 22 (2018), no. 1, 323-437.
- Curve counting on K3 x E, the Igusa cusp form chi_10, and descendent integration (with Rahul Pandharipande)
K3 surfaces and their moduli, Birkhauser Prog. in Math. 315, 245-278, 2014.
- Curve counting on abelian surfaces and threefolds (with Jim Bryan, Rahul Pandharipande, and Qizheng Yin)
Algebraic Geometry, 5 (2018), no. 4, 398-463.
- Gromov-Witten theory of K3 x P1 and quasi-Jacobi forms
International Mathematics Research Notices, Vol. 2019, Issue 16, 4966-5011.
- On reduced stable pair invariants
Mathematische Zeitschrift, 289 (2018), no. 1-2, 323-353.
- Curve counting on elliptic Calabi-Yau threefolds via derived categories (with Junliang Shen)
Journal of the European Mathematical Society, to appear, 2016.
- Holomorphic anomaly equations and the Igusa cusp form conjecture (with Aaron Pixton)
Inventiones mathematicae, 213 (2018), no. 2, 507-587.
- Reduced Donaldson-Thomas invariants and the ring of dual numbers (with Junliang Shen)
Proceedings of the London Mathematical Society, (3) 118 (2019), no. 1, 191-220.
- Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations (with Aaron Pixton)
Geometry & Topology, 23 (2019), no. 3, 1415-1489.
- Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants (with Junliang Shen and Qizheng Yin)
Advances in Mathematics, Volume 357, to appear, 2019.
Submitted papers and preprints:
- A Serre derivative for even weight Jacobi forms, 2012.
- Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
with Dulip Piyaratne and Yukinobu Toda, 2018.
- CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms
with Jim Bryan, and containing a joint Appendix with Sheldon Katz, 2018.
- Elliptic curves in Hyperkähler varieties
with Denis Nesterov, 2019.
- Automorphisms of Hilbert schemes of points on surfaces
with Pieter Belmans, Jorgen Vold Rennemo, 2019.
- A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface, 2019.
- A program for calculating the number of polarized isogenies of abelian varieties. Used in Curve counting on abelian surfaces and threefolds.
- The code used for the calculations in the Appendix of Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions.
- PhD Thesis
- Seminar Algebraic Geometry
- Seminar: Quantum Groups Quantum Cohomology of Symplectic Varieties (Fall 2019, with C. Stroppel)
- Seminar: Beyond GIT (Fall 2018)
- Moduli and Representation Theory seminar (MSRI, Spring 2018)
- Motivic PT Seminar Fall 2014
- Hausdorff School Perverse Sheaves in Enumerative Geometry, February 10-14, 2019.
- Bethe Forum Number Theoretic Methods in Quantum Physics, July 15 - 19, 2019.
- Complex Geometry Group
- Co-authors: Pieter Belmans, Jim Bryan, Sheldon Katz, Denis Nesterov, Rahul Pandharipande, Aaron Pixton, Dulip Piyaratne, Jørgen Vold Rennemo, Junliang Shen, Yukinobu Toda, Qizheng Yin.