Georg Oberdieck

Welcome to my homepage! I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics. In the Summer 2021 I teach a class on Gromov-Witten theory of hyperkähler varieties. I also organize a seminar on Enumerative Geometry, viewed in a broad sense.

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, to appear, 2019.
  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, to appear, 2019.
  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.

Submitted papers and preprints:

  1. A Serre derivative for even weight Jacobi forms, 2012.
  2. Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
    with Dulip Piyaratne and Yukinobu Toda, 2018.
    The code used for the calculations in the Appendix.
  3. Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces
    with Thorsten Beckmann, 2020.
  4. On equivariant derived categories
    with Thorsten Beckmann, 2020.
  5. Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties, 2021. SageCode for Fano and DV case.

Other:

  1. PhD Thesis
  2. Notes on the monodromy of K3[n]-Hyperkahler (after Markman)

Teaching:

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

Seminars:

  1. Algebraic Geometry, Physics, Gromov-Witten theory Seminar (Fall 2020+)
  2. Seminar Algebraic Geometry
  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. Moduli and Representation Theory seminar (MSRI, Spring 2018)
  7. Motivic PT Seminar Fall 2014

Supervised theses: See here

Conferences:

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

Links:

  1. Complex Geometry Group
  2. 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.

Photos