# 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 MathematikWinterthurerstrasse 190CH-8057 ZürichSwitzerland Office Y27K42

Teaching

MAT773 - Topics in convex geometry (Fall term 2021)

MAT007 - Introduction to computer algebra and mathematical programming (Spring term 2022)

MAT952 - Expander graphs (Fall term 2021)

Research Interests

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

Algebraic geometry
• Logarithmic double ramification cycles (joint with D. Holmes, S. Molcho, R. Pandharipande, A. Pixton)
Preprint (2022) - preprint
• Étale cohomological stability of the moduli space of stable elliptic surfaces (joint with O. Banerjee, J.-Y. Park)
Preprint (2022) - preprint
• Integrals of $$\psi$$-classes on twisted double ramification cycles and spaces of differentials (joint with M. Costantini, A. Sauvaget)
Preprint (2021) - preprint
• 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)
Mathematical Proceedings of the Cambridge Philosophical Society, 173.3 (2022) - preprint, journal version
• 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)
Forum of Math: Sigma (2022) - preprint, journal version
• 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)
Journal of Software for Algebra and Geometry, 11.1 (2021) - preprint, journal version
• 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 Counting and Cayley Graph Expanders (joint with N. Peyerimhoff, M. Roth, J. Stix, A. Vdovina, P. Wellnitz)**
accepted in SIAM J. Discrete Math (SIDMA)
• 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, SIAM Journal on Computing (SICOMP) 2022 - preprint, conference version, journal version
• Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness (joint with J. Dörfler, M. Roth, P. Wellnitz)
MFCS conference 2019, Algorithmica, 84. (2022) - preprint, conference version, journal 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
** This journal article is a combination of the two conference papers submitted to MFCS 2021 and ICALP 2021.

Lecture notes

The moduli space of curves (Summer 2020)

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

1. Operators of Cowen-Douglas class, Bachelor thesis, 2012
2. The Toric Variety $$\text{Bl}_{n+1} \mathbb{P}^n$$ and its Associated Secondary Fan, Master thesis, 2014
3. A poster concerning the moduli spaces of self-maps of $$\mathbb{CP}^1$$, presented at the AMS Summer Institute 2015 in Salt Lake City
4. A poster about spaces of twisted $$k$$-differentials, presented at the GAeL-conference 2017 in Bath
5. Slides from a beamer talk about a conjectural relation of moduli spaces of twisted $$k$$-differentials and Pixton's class
6. Slides from my PhD defense talk
7. A talk about the relation between strata of k-differentials and double ramification cycles
8. Another talk about the relation between strata of k-differentials and double ramification cycles
9. An (interactive) talk about the software package admcycles, given in Zurich
10. Another (interactive) talk about the software package admcycles, given in Leiden
11. A talk about a paper by Pandharipande-Yin about relations in the Chow group of the moduli of K3 surfaces
12. A talk about intersection numbers of psi-classes with strata of k-differentials and double ramification cycles (joint with M. Costantini, A. Sauvaget)
13. A guide on how to get started using SageMath
14. A talk about logarithmic double ramification cycles (joint with D. Holmes, S. Molcho, R. Pandharipande, A. Pixton)