Johannes Schmitt

I am a Postdoc at the University of Zürich working with Andrew Kresch. Before this, I was a PhD student of Rahul Pandharipande at ETH Zürich and a Postdoc in Bonn working with Daniel Huybrechts. My CV can be found here.

Contact

Email	johannes.schmitt@math.uzh.ch
Phone	+41 44 635 58 78
Adress	Institut für Mathematik Winterthurerstrasse 190 CH-8057 Zürich Switzerland
Office	Y27K42

Teaching

MAT952 - Expander graphs (Fall term 2021)

V5A4 - Selected Topics in Algebraic Geometry - The moduli space of curves (Summer term 2020)

Research Interests

Algebraic geometry, Moduli spaces of curves, Geometric Invariant Theory, Algebraic stacks, Tautological cycles, Hurwitz spaces, Chow groups

Papers/Preprints

Algebraic geometry

Arithmetic geometry of the moduli stack of Weierstrass fibrations over \(\mathbb{P}^1\) (joint with J.-Y. Park)
Preprint (2021) - preprint
Tevelev degrees and Hurwitz moduli spaces (joint with A. Cela, R. Pandharipande)
Preprint (2021) - preprint
The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves (joint with S. Molcho, R. Pandharipande)
Preprint (2021) - preprint
Chow rings of stacks of prestable curves I (joint with Y. Bae, appendix joint with J. Skowera)
Preprint (2020) - preprint
Chow rings of stacks of prestable curves II (joint with Y. Bae)
Preprint (2020*) - preprint
Pixton's formula and Abel-Jacobi theory on the Picard stack (joint with Y. Bae, D. Holmes, R. Pandharipande, R. Schwarz)
Preprint (2020), accepted in Acta Mathematica - preprint
admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves (joint with V. Delecroix, J. van Zelm)
Preprint (2020), accepted in Journal of Software for Algebra and Geometry - preprint
Infinitesimal structure of the pluricanonical double ramification locus (joint with D. Holmes)
Compositio Mathematica, 157 (2021) - preprint, journal version
Zero cycles on moduli spaces of curves (joint with R. Pandharipande)
Épijournal de Géométrie Algébrique, 4. (2020) - preprint, journal version
Intersections of loci of admissible covers with tautological classes (joint with J. van Zelm)
Selecta Mathematica, 26. (2020) - preprint, journal version
Multiplicativity of the double ramification cycle (joint with D. Holmes, A. Pixton)
Documenta Mathematica, 24. (2019) - preprint, journal version
A correspondence of good G-sets under partial geometric quotients
Beiträge zur Algebra und Geometrie, 59.2 (2018) - preprint, journal version
Dimension theory of the moduli space of twisted k-differentials
Documenta Mathematica, 23. (2018) - preprint, journal version
A compactification of the moduli space of self-maps of \(\mathbb{CP}^1\) using stable maps
Conformal Geometry and Dynamics, 21. (2017) - preprint, journal version

* parts I and II of this preprint originally appeared as a single paper in 2020 and were split in 2021

Other subjects

Parameterized (Modular) Counting and Cayley Graph Expanders (joint with N. Peyerimhoff, M. Roth, J. Stix, A. Vdovina)
MFCS conference 2021 - preprint
Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders (joint with M. Roth, P. Wellnitz)
ICALP conference 2021 - preprint
Counting Small Induced Subgraphs Satisfying Monotone Properties (joint with M. Roth, P. Wellnitz)
FOCS conference 2020 - preprint, conference version
Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness (joint with J. Dörfler, M. Roth, P. Wellnitz)
MFCS conference 2019 - preprint, conference version
Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness (joint with M. Roth)
IPEC conference 2018 (Best Paper Award and Best Student Paper Award), Algorithmica, 82. (2020) - preprint, journal version
Cowen-Douglas operators and dominating sets (joint with J. Eschmeier)
Journal of Operator Theory, 1. (2014) - preprint, journal version

Lecture notes

The moduli space of curves (Summer 2020)

admcycles
A Sage package for calculations in the tautological ring of \(\overline{\mathcal{M}}_{g,n}\) and computation of cycles of admissible covers (joint with V. Delecroix, J. van Zelm)

Organization

Hausdorff school “Perverse Sheaves in Enumerative Geometry” (February 10-14, 2020).
Online working seminar “Smooth compactifications and bChow intersections via blowups/subdivisions” (Summer 2020).

Some Links & Files

Operators of Cowen-Douglas class, Bachelor thesis, 2012
The Toric Variety \(\text{Bl}_{n+1} \mathbb{P}^n\) and its Associated Secondary Fan, Master thesis, 2014
A poster concerning the moduli spaces of self-maps of \(\mathbb{CP}^1\), presented at the AMS Summer Institute 2015 in Salt Lake City
A poster about spaces of twisted \(k\)-differentials, presented at the GAeL-conference 2017 in Bath
Slides from a beamer talk about a conjectural relation of moduli spaces of twisted \(k\)-differentials and Pixton's class
Slides from my PhD defense talk
A talk about the relation between strata of k-differentials and double ramification cycles
Another talk about the relation between strata of k-differentials and double ramification cycles
An (interactive) talk about the software package admcycles, given in Zurich
Another (interactive) talk about the software package admcycles, given in Leiden
A talk about a paper by Pandharipande-Yin about relations in the Chow group of the moduli of K3 surfaces
A talk about intersection numbers of psi-classes with strata of k-differentials and double ramification cycles (joint with M. Costantini, A. Sauvaget)