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:

1. Gromov-Witten invariants of the Hilbert scheme of points of a K3 surface
   Geometry & Topology, 22 (2018), no. 1, 323-437.
2. 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.
3. 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.
4. Gromov-Witten theory of K3 x P1 and quasi-Jacobi forms
   International Mathematics Research Notices, Vol. 2019, no. 16, 4966-5011.
5. On reduced stable pair invariants
   Mathematische Zeitschrift, 289 (2018), no. 1-2, 323-353.
6. 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.
7. Holomorphic anomaly equations and the Igusa cusp form conjecture (with Aaron Pixton)
   Inventiones mathematicae, 213 (2018), no. 2, 507-587.
8. 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.
9. Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations (with Aaron Pixton)
   Geometry & Topology, 23 (2019), no. 3, 1415-1489.
10. 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.
11. 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.
12. Elliptic curves in Hyperkähler varieties (with Denis Nesterov)
    International Mathematics Research Notices, 2021, no. 4, 2962-2990.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces (with Thorsten Beckmann)
    Algebraic Geometry, 9 (2022), no. 4, 400-442.
19. 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.
20. 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.
21. 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.
22. Universality of descendent integrals on moduli spaces of stable sheaves on K3 surfaces
    SIGMA 18 (2022), 076, 15 pages
23. On equivariant derived categories (with Thorsten Beckmann)
    European Journal of Mathematics 9 (2023), no. 2, Paper No. 36, 39 pp.
24. Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
    Geometry & Topology, to appear.
25. Multiple cover formulas for K3 geometries, wallcrossing, and Quot schemes
    Geometry & Topology, to appear.
26. Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds (with Yalong Cao and Yukinobu Toda)
    Communications in Mathematical Physics, to appear.
27. Curve counting on the Enriques surface and the Klemm-Marino formula
    Journal of the European Mathematical Society, to appear.
28. Marked relative invariants and GW/PT correspondences
    Advances in Mathematics, to appear.

Preprints:

29. Lagrangian Planes hyperkahler varieties of K3[n]-type, 2022
30. On the descendent Gromov-Witten theory of a K3 surface, 2023. Code for computating GW invariants of K3: GWK3
31. Pandharipande-Thomas theory of elliptic threefolds, quasi-Jacobi forms and holomorphic anomaly equations
    with Maximilian Schimpf, 2023.
32. Quantum cohomology of the Hilbert scheme of points on an elliptic surface
    with Aaron Pixton, 2023.

Other writings:

1. PhD Thesis
2. A Serre derivative for even weight Jacobi forms. Unpublished Note., 2012.
3. Notes on the monodromy of K3[n]-Hyperkahler (after Markman)
4. Oberwolfach report: Curves on the Hilbert scheme of a K3 surface
5. Oberwolfach report: Noether-Lefschetz theory of hyper-Kähler varieties via Gromov-Witten invariants
6. On the Chern character numbers of the Hilbert scheme of points on a K3 surface
7. 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.
8. Notes on the LLV decomposition (joint with Jieao Song)
9. Lectures on holomorphic anomaly equations (for Swampland workshop)
10. Notes of talk "Curve counting on the Enriques surface and the Klemm-Marino formula"
11. A remark on the Banana Calabi-Yau threefold

PhD students:

1. Maximilian Schimpf

Former students and supervised theses

Past lectures:

1. K3 surfaces
2. Gromov-Witten theory of hyperkähler varieties (Summer 2021)
3. Algebraic Stacks (Fall 2020)
4. Topics in Enumerative Geometry (Fall 2019)
5. Algebraic Geometry II (Spring 2019)
6. Algebraic Geometry I (Fall 2018)

Past student seminars:

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

Research seminar organization:

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

Conferences:

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

Links:

1. Google Scholar
2. KTH & SU Algebra and Geometry Seminar
3. 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.
4. Poonen's suggestions on mathematical writing

Photos