M.Sc. Johannes Schwab

Research

My research is currently centered around the moduli space of (k-)differentials on Riemann surfaces. In particular I study questions related to its topology and the topology of linear submanifolds.

Preprints

Diffstrata

Diffstrata is a software package for intersection therory computations in the tautological ring of strata of k-differentials. Diffstrata is written in SageMath and is build on and part of admcycles. Diffstrata was originally developed for strata of abelian differentials by M. Costantini, M. Möller and J. Zachhuber and was extended to strata of k-differentials in joint work with M. Costantini and M. Möller.

Get diffstrata

The version of diffstrata that comes with the current official release of admcycles can only handle strata of abelian differentials. If that is all you need the best way to proceed is to follow the instructions for installing admcycles here.

To obtain a version of admcycles which includes a version of diffstrata that can handle k-differentials, you can download this zip archive, unpack it and start sage in the newly created folder.

Example computation

Here is an example how to compute the dimension, the Euler characteristic and the Masur-Veech volume of the projectivized stratum of quadratic differentials with signature (-1,5).

sage: from admcycles.diffstrata import Stratum
sage: X = Stratum((-1,5), 2)
sage: X.dim()
3
sage: X.euler_characteristic()
-7/15
sage: X.masur_veech_volume()
28/135*pi^4

This CoCalc notebook contains some more examples and details.

Lehre