Georg Oberdieck

Welcome to my homepage! I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics. A small research seminar on enumerative geometry and moduli spaces can be found here here. In the summer 2022 I organize a student seminar on Hilbert schemes of points and infinite dimensional Lie algebras.

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:

  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.
    A 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 containing a 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), to appear, 2019.
  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, to appear, 2020.
    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, to appear.
    The 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, to appear, 2020.
  19. Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties
    Forum Sigma, to appear, 2021. 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
    PAMQ, to appear.

Submitted papers and preprints:

  1. On equivariant derived categories
    with Thorsten Beckmann, 2020.
  2. Universality of descendent integrals on moduli spaces of stable sheaves on K3 surfaces, 2021
  3. Multiple cover formulas for K3 geometries, wallcrossing, and Quot schemes, 2021
  4. Marked relative invariants and GW/PT correspondences, 2021
  5. Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
    with Yalong Cao and Yukinobu Toda, 2022
  6. Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
    with Yalong Cao and Yukinobu Toda, 2022
  7. Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface, 2022
  8. Lagrangian Planes hyperkahler varieties of K3[n]-type, 2022

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)

PhD students:

  1. Denis Nesterov
  2. Maximilian Schimpf

Supervised theses: See here

Teaching:

  1. Seminar on Donaldson-Thomas theory (Fall 2021)
  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)

Seminars:

  1. Hilbert schemes of points and infinite dimensional Lie algebras (Sommersemester 2022)
  2. Algebraic Geometry, Physics, Gromov-Witten theory Seminar (Fall 2020+)
  3. Seminar Algebraic Geometry
  4. Hilbert schemes and applications, Sommer 2020
  5. Quantum Groups & Quantum Cohomology of Symplectic Varieties (Fall 2019, with C. Stroppel)
  6. Beyond GIT (Fall 2018)
  7. Moduli and Representation Theory seminar (MSRI, Spring 2018)
  8. Motivic PT Seminar Fall 2014

Conferences:

  1. Curves and K3 surfaces
  2. Hausdorff School Perverse Sheaves in Enumerative Geometry, February 10-14, 2020.
  3. Bethe Forum Number Theoretic Methods in Quantum Physics, July 15 - 19, 2019.

Links:

  1. Google Scholar
  2. Complex Geometry Group
  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, Junliang Shen, Jieao Song, Yukinobu Toda, Claire Voisin, Qizheng Yin.
  4. Poonen's suggestions on mathematical writing

Photos