## Georg Oberdieck

Welcome to my homepage! I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics. In the Fall 2021 I organize a seminar on Donaldson-Thomas theory. A small research seminar on topics around enumerative geometry, K3 surfaces and moduli spaces can be found here here.

**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.

A SAGE program for calculating the number of polarized isogenies of abelian varieties. - 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*, 2021, no. 4, 2962–2990. - 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*96 (2021), no. 1, 65--77. - Motivic decompositions for the Hilbert scheme of points of a K3 surface

with Andrei Negut and Qizheng Yin*Journal für die Reine und Angewandte Mathematik (Crelle's journal)*, to appear, 2019. - Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms

with Jan-Willem van Ittersum and Aaron Pixton

*Selecta Mathematica*, to appear, 2020.

SAGE code used in computations. - Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions

with Dulip Piyaratne and Yukinobu Toda.

*Journal of Algebraic Geometry*, to appear.

The code used for the calculations in the Appendix. - Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces

with Thorsten Beckmann*Algebraic Geometry*, to appear, 2020.

**Submitted papers and preprints:**

- A Serre derivative for even weight Jacobi forms, 2012.
- On equivariant derived categories

with Thorsten Beckmann, 2020. - Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties, 2021. SageCode for Fano and DV case.
- Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds

with Jieao Song and Claire Voisin, 2021. - Universality of descendent integrals on moduli spaces of stable sheaves on K3 surfaces, 2021
- Multiple cover formulas for K3 geometries, wallcrossing, and Quot schemes, 2021

**Other writings:**

- PhD Thesis
- Notes on the monodromy of K3[n]-Hyperkahler (after Markman)
- Oberwolfach report: Curves on the Hilbert scheme of a K3 surface
- Oberwolfach report: Noether-Lefschetz theory of hyper-Kähler varieties via Gromov-Witten invariants
- On the Chern character numbers of the Hilbert scheme of points on a K3 surface
- Slides for the talk Kaneko-Zagier equations for Jacobi forms and curve counting on CHL manifolds at the Quantum Gravity & Modularity Workshop in Dublin, May 2021.
- Notes on the LLV decomposition (joint with Jieao Song)

**PhD students:**

- Denis Nesterov
- Maximilian Schimpf

**Supervised theses:** See here

**Teaching:**

- Seminar on Donaldson-Thomas theory (Fall 2021)
- Gromov-Witten theory of hyperkähler varieties (Summer 2021)
- 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

**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, Jieao Song, Yukinobu Toda, Claire Voisin, Qizheng Yin.
- Poonen's suggestions on mathematical writing