Winter School on Enumerative Geometry and Modular Forms

February 11 - 15, 2019,  Frankfurt am Main

Organised by: Martin Möller und Martin Ulirsch

Supported by LOEWE

All talks will take place in the Insitut for Mathematics in lecture room "Hilbertraum", Room 302 in Robert-Mayer-Strasse 8.
Access to the Insitut for Mathematics is from Robert-Mayer Strasse 8., see number 18 on the map.

The Conference dinner takes place on Thursday, Feb 14th at 18:15 pm at

Minicourses (3h)

  • Emily Clader (San Francisco State University): Introduction to Gromov-Witten-theory (Exercises)
  • Felix Janda (University of Michigan): Tautological rings and the double ramification cycle (Lecture Notes)
  • Georg Oberdieck (MIT/University of Bonn): Modular forms in enumerative geometry

Research Talks

[Download: abstracts.pdf]

  • Kathrin Bringmann (University of Köln): False theta functions and their modular properties.

    In my talk I will discuss modular properties of false theta functions. Due to a wrong sign
    factor these are not directly seen to be modular, however there are ways to repair this. I will
    report about this in my talk.

  • Emily Clader (San Francisco State University): Wall-crossing in quasimap theory

    Quasimaps are a generalization of stable maps that depend on the additional datum of a
    positive rational number epsilon. The dependence of the theory on epsilon is encoded in
    certain wall-crossing formulas, first conjectured by Ciocan-Fontanine and Kim and since
    proved in many cases, which are intimately related to the subject of mirror symmetry. I
    will discuss quasimap theory and describe an alternative proof of Ciocan-Fontanine–Kim’s
    wall-crossing theorem for all-genus quasimaps to complete intersections in projective space;
    this proof has the advantage that it can be adapted to prove an analogous theorem in the more
    general context of certain "gauged linear sigma models." This is joint work with Felix Janda
    and Yongbin Ruan.

  • Felix Janda (University of Michigan): Variants of the DR cycle

    In this talk I want to discuss two variants of the double ramification cycle. One is a DR cycle
    twisted over a base manifold X. The other is a DR cycle twisted by a power of the dualizing
    sheaf, and is closely related to strata of meromorphic differentials. This is based on work joint
    with R. Pandharipande, A. Pixton and D. Zvonkine.

  • Martijn Kool (Utrecht University): New calculations in Vafa-Witten theory

    In the 1990’s, Vafa-Witten tested S-duality of N = 4 supersymmetric Yang-Mills theory on a
    complex algebraic surface by studying modularity of a certain partition function. Recently, a
    mathematical definition of Vafa-Witten’s invariants was given by Tanaka-Thomas. I outline
    a method for calculating the instanton contribution to these invariants using Mochizuki’s
    theory of algebraic Donaldson invariants. For SU(2), this leads to verifications of Vafa-Witten’s
    original formula. For SU(3), we find a new formula which corrects an error in the physics
    literature. I will also discuss refinements to virtual Xy genus, elliptic genus, and cobordism
  • Hyenho Lho (ETH Zürich): Quasi-modularity of Calabi-Yau fibration

    Quasi-modularity and holomorphic anomaly equations were conjectured for Gromov-Witten
    invariants of elliptic fibrations by Oberdieck and Pixton. I will discuss the generalisation of
    this conjectures to higher dimensional Calabi-Yau fibrations and prove some partial results of
    the conjectures for Calabi-Yau manifolds given by hypersurface in some toric varieties.

  • Cristina Manolache (Imperial College): A splitting of the virtual class

    One of the main computational tools in genus zero Gromov–Witten theory is Quantum
    Lefschetz. Quantum Lefschetz fails for higher genus invariants. I will show how to split the
    virtual class of the moduli space of genus one stable maps and discuss applications of this
    splitting. This is based on joint work with Tom Coates.

  • Georg Oberdieck (MIT/University of Bonn): The Gromov-Witten theory of T*ExP1

    I will explain how to compute the Gromov-Witten theory of the product of the cotangent
    bundle of an elliptic curve with the projective line, relative to fibers over the P1. The answer is
    expressed in terms of an operator on Fock space and quasi-Jacobi forms. Joint work with A. Pixton.

  • Nicola Pagani (University of Liverpool):
    Towards an enumerative geometry of compactified universal Jacobians

    We will discuss some results on enumerative geometry calculations on compactified universal
    Jacobians, and their relation to the well-studied enumerative geometry of Mg,n, the moduli
    space of stable pointed curves. The main new phenomenon (compared to Mg,n) is that the
    compactification of the Jacobian depends on a polarization parameter, so the challenge is to
    produce wall-crossing formulae. Most results are obtained in collaboration with Jesse Kass
    (University of South Carolina).

  • Adrian Sauvaget (Jussieu): Masur-Veech volume recursion

    We will present a recursion for Masur-Veech volumes. One of the important step in the proof
    of this formula is to show that the connected q-bracket from the algebra of shifted symmetric
    function can partially be computed inductively.

  • Dmitry Zvonkine (Jussieu): Cohomological field theories with non-tautological classes

    We construct the first known example of a cohomological field theory that takes values not
    only in the tautological cohomology ring of the moduli space, but also in the non-tautological
    part. This is a joint work with Rahul Pandharipande.

Practical Information:

  • Map of campus Bockenheim.
  • To get to the lecture room from Frankfurt Main Station you can either walk (20-25 min), take the subway U4 to Bockenheimer Warte or the tram 16 or 17 to Varrentrappstraße. Time table at RMV as well as information about tickets.
  • There are plenty of places to eat nearby, e.g., in Leipziger Strasse, Kiesstrasse, ... . Moreover, on Thursday there is the weekly market at Bockenheimer Warte.
  • Room: the workshop will take place in Hilbertraum, Room 302 in Robert-Mayer-Strasse 6-8.


If you are interested in participating please send an informal email to

- Deadline for funding has passed. -

Application deadline: November 1, 2018