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
- Ristorante la Contessa
60486 Frankfurt am Main
- 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
- 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.
- 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