Welcome to my homepage!
I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics.
In the Fall 2018 I teach Algebraic Geometry I.
Algebraic Geometry, in particular Gromov-Witten theory, Donaldson-Thomas theory and K3 surfaces.
Modular and Jacobi forms.
Phone: +49 228 736 2271
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, in 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, to appear, 2016.
- 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, to appear, 2016.
- Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
with Aaron Pixton, Geometry & Topology, to appear, 2017.
Submitted papers and preprints:
- A Serre derivative for even weight Jacobi forms, 2012.
- Rational curves in the Fano varieties of cubic 4-folds and Gromov-Witten invariants
with Junliang Shen and Qizheng Yin, 2018.
- 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.
- 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: Beyond GIT (Fall 2018)
- Seminar Algebraic Geometry
- Complex Geometry Group
- MSRI Modul and Representation Theory seminar
- Motivic PT Seminar Fall 2014
- Co-authors: Jim Bryan, Sheldon Katz, Rahul Pandharipande, Aaron Pixton, Dulip Piyaratne, Junliang Shen, Yukinobu Toda, Qizheng Yin,