Georg Oberdieck
Welcome to my homepage! I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics.

Contact:
Email: georgo@math.uni-bonn.de
Phone: +49 228 73-62271
Office: Endenicher Allee 60, 1.028
Address:
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D-53115 Bonn
Research Interests:
Algebraic Geometry, in particular K3 surfaces, holomorphic-symplectic varieties, Hilbert schemes of points, Gromov-Witten and Donaldson-Thomas theory. Modular and Jacobi forms.
Papers:
- 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, no. 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, 22 (2020), no. 3, 967-1002. - 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 (2019), 106829, 8 pp. - Automorphisms of Hilbert schemes of points on surfaces
with Pieter Belmans and Jorgen Vold Rennemo
Transactions of the American Mathematical Society, 373 (2020), no. 9, 6139–6156. - Elliptic curves in Hyperkähler varieties (with Denis Nesterov)
International Mathematics Research Notices, to appear, 2019. - CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms
with Jim Bryan, and containing a joint Appendix with Sheldon Katz
Communications in Number Theory and Physics, 14 (2020), no. 4, 785–862. - A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface
Commentarii Mathematici Helvetici, 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. - Motivic decompositions for the Hilbert scheme of points of a K3 surface
with Andrei Negut and Qizheng Yin, 2019. - Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
with Thorsten Beckmann, 2020. - On equivariant derived categories
with Thorsten Beckmann, 2020. - Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms
with Jan-Willem van Ittersum and Aaron Pixton, 2020. SAGE code used in computations. - Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties, 2021. SageCode for Fano and DV case.
Files:
- 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
- A few notes on the monodromy of K3[n]-Hyperkahler (after Markman)
Past Teaching:
- Algebraic Stacks (Fall 2020)
- Topics in Enumerative Geometry (Fall 2019)
- Algebraic Geometry II (Spring 2019)
- Algebraic Geometry I (Fall 2018)
Seminars:
- Algebraic Geometry, Physics, Gromov-Witten theory Seminar (Fall 2020+)
- Seminar Algebraic Geometry
- Hilbert schemes and applications, Sommer 2020
- Quantum Groups & Quantum Cohomology of Symplectic Varieties (Fall 2019, with C. Stroppel)
- Beyond GIT (Fall 2018)
- Moduli and Representation Theory seminar (MSRI, Spring 2018)
- Motivic PT Seminar Fall 2014
Supervised theses: See here
Conferences:
- Hausdorff School Perverse Sheaves in Enumerative Geometry, February 10-14, 2020.
- Bethe Forum Number Theoretic Methods in Quantum Physics, July 15 - 19, 2019.
Links:
- Complex Geometry Group
- Co-authors: Thorsten Beckmann, Pieter Belmans, Jim Bryan, Jan-Willem van Ittersum, Sheldon Katz, Andrei Negut, Denis Nesterov, Rahul Pandharipande, Aaron Pixton, Dulip Piyaratne, Jørgen Vold Rennemo, Junliang Shen, Yukinobu Toda, Qizheng Yin.