Welcome! I am an associate professor at KTH in the Department of Mathematics.

**Contact:**

Email: georgo@kth.se

Phone: +46-8-790-6688

Office: Lindstedtsvägen 25, 3549

**Address**:

KTH Royal Institute of Technology

Georg Oberdieck

Department of Mathematics

SE - 100 44 Stockholm

Sweden

**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. 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 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)*, 778 (2021), 65-95. - Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms (with Jan-Willem van Ittersum and Aaron Pixton)

*Selecta Mathematica*, (N.S.) 27 (2021), no. 4, Paper No. 64, 30 pp. 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*, 31 (2022), no. 1, 13-73. Sage 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*, 9 (2022), no. 4, 400-442. - Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties

*Forum Sigma*, 10 (2022), Paper No. e21, 46 pp. 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)

*Pure and Applied Mathematics Quarterly*18 (2022), no. 4, 1723-1748. - Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds (with Yalong Cao and Yukinobu Toda)

*Advances in Mathematics*408 (2022), part B, Paper No. 108605, 44 pp. - Universality of descendent integrals on moduli spaces of stable sheaves on K3 surfaces
*SIGMA*18 (2022), 076, 15 pages - On equivariant derived categories (with Thorsten Beckmann)

*European Journal of Mathematics*9 (2023), no. 2, Paper No. 36, 39 pp. - Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
*Geometry & Topology*, to appear. - Multiple cover formulas for K3 geometries, wallcrossing, and Quot schemes
*Geometry & Topology*, to appear. - Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds (with Yalong Cao and Yukinobu Toda)

*Communications in Mathematical Physics*, to appear. - Curve counting on the Enriques surface and the Klemm-Marino formula

*Journal of the European Mathematical Society*, to appear. - Marked relative invariants and GW/PT correspondences
*Advances in Mathematics*, to appear.

**Preprints:**

- Lagrangian Planes hyperkahler varieties of K3[n]-type, 2022
- On the descendent Gromov-Witten theory of a K3 surface, 2023. Code for computating GW invariants of K3: GWK3
- Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations

with Maximilian Schimpf, 2023. - Quantum cohomology of the Hilbert scheme of points on an elliptic surface

with Aaron Pixton, 2023.

**Other writings:**

- PhD Thesis
- A Serre derivative for even weight Jacobi forms. Unpublished Note., 2012.
- 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)
- Lectures on holomorphic anomaly equations (for Swampland workshop)
- Notes of talk "Curve counting on the Enriques surface and the Klemm-Marino formula"
- A remark on the Banana Calabi-Yau threefold

**PhD students:**

- Maximilian Schimpf

**Former students and supervised theses**

**Past lectures:**

- K3 surfaces
- 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)

**Past student seminars:**

- Hilbert schemes of points and infinite dimensional Lie algebras (Sommersemester 2022)
- Seminar on Donaldson-Thomas theory (Fall 2021)
- Hilbert schemes and applications, Sommer 2020
- Quantum Groups & Quantum Cohomology of Symplectic Varieties (Fall 2019, with C. Stroppel)
- Beyond GIT (Fall 2018)
- Motivic PT Seminar (Fall 2014)

**Research seminar organization:**

- Seminar Algebraic Geometry (2018-)
- Algebraic Geometry, Physics, Gromov-Witten theory Seminar (2020-2022)
- Moduli and Representation Theory seminar (MSRI, Spring 2018)

**Conferences:**

- Workshop Enumerative geometry of moduli spaces of sheaves, Sep 18/19, 2023, KTH
- Workshop Curves and K3 surfaces, May 9-12, 2022, Bonn.
- Hausdorff School Perverse Sheaves in Enumerative Geometry, February 10-14, 2020, Bonn.
- Bethe Forum Number Theoretic Methods in Quantum Physics, July 15 - 19, 2019, Bonn.

**Links:**

- Google Scholar
- KTH & SU Algebra and Geometry Seminar
- Co-authors: Thorsten Beckmann, Pieter Belmans, Jim Bryan, Yalong Cao, Jan-Willem van Ittersum, Sheldon Katz, Andrei Negut, Denis Nesterov, Rahul Pandharipande, Aaron Pixton, Dulip Piyaratne, Jørgen Vold Rennemo, Maximilian Schimpf, Junliang Shen, Jieao Song, Yukinobu Toda, Claire Voisin, Qizheng Yin.
- Poonen's suggestions on mathematical writing