Georg Oberdieck

Welcome to my homepage!

I am a Bonn Junior Fellow at the Hausdorff Center for Mathematics.

In the Fall 19 I teach a class on Topics in Enumerative Geometry.


Research Interests:

Algebraic Geometry, in particular K3 surfaces, holomorphic-symplectic varieties, Gromov-Witten theory, Donaldson-Thomas theory.
Modular and Jacobi forms.


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


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.
  4. Gromov-Witten theory of K3 x P1 and quasi-Jacobi forms
    International Mathematics Research Notices, Vol. 2019, Issue 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, to appear, 2016.
  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, to appear, 2019.

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.
  3. CHL Calabi-Yau threefolds: Curve counting, Mathieu moonshine and Siegel modular forms
    with Jim Bryan, and containing a joint Appendix with Sheldon Katz, 2018.
  4. Elliptic curves in Hyperkähler varieties
    with Denis Nesterov, 2019.
  5. Automorphisms of Hilbert schemes of points on surfaces
    with Pieter Belmans, Jorgen Vold Rennemo, 2019.
  6. A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface, 2019.

Files:

  1. A program for calculating the number of polarized isogenies of abelian varieties. Used in Curve counting on abelian surfaces and threefolds.
  2. The code used for the calculations in the Appendix of Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions.
  3. PhD Thesis

Past Teaching:

  1. Algebraic Geometry II (Spring 2019)
  2. Algebraic Geometry I (Fall 2018)

Seminars:

  1. Seminar Algebraic Geometry
  2. Seminar: Quantum Groups Quantum Cohomology of Symplectic Varieties (Fall 2019, with C. Stroppel)
  3. Seminar: Beyond GIT (Fall 2018)
  4. Moduli and Representation Theory seminar (MSRI, Spring 2018)
  5. Motivic PT Seminar Fall 2014

Conferences:

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

Links:

  1. Complex Geometry Group
  2. Co-authors: Pieter Belmans, Jim Bryan, Sheldon Katz, Denis Nesterov, Rahul Pandharipande, Aaron Pixton, Dulip Piyaratne, Jørgen Vold Rennemo, Junliang Shen, Yukinobu Toda, Qizheng Yin.

Photos