Johannes Schmitt
I am a SwissMAP Research Fellow at the ETH Zürich. Before this, I was a PhD student of Rahul Pandharipande at ETH Zürich, and a Postdoc in Bonn (with Daniel Huybrechts) and Zürich (with Andrew Kresch). My CV can be found here.
Contact
Email |
johannes.schmitt@math.ethz.ch |
Phone |
+41446323136 |
Adress |
Department Mathematik Rämistrasse 101 CH-8092 Zürich Switzerland |
Office |
HG J16.1 |
Teaching
MAT016 - Proofs from The Book (Spring term 2023)
MAT773 - Topics in convex geometry (Fall term 2022)
MAT007 - Introduction to computer algebra and mathematical programming (Spring term 2022)
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
- Birational classification of toric orbifolds
Preprint (2023) - preprint
- A tale of two moduli spaces: logarithmic and multi-scale differentials
(joint with D. Chen, S. Grushevsky, D. Holmes, M. Möller)
Preprint (2022) - preprint
- 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)
Compositio Mathematica, 159.2 (2023) - preprint, journal version
- 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)
Journal für die reine und angewandte Mathematik (Crelles Journal) (2023) - preprint, journal version
- Pixton's formula and Abel-Jacobi theory on the Picard stack (joint with Y. Bae, D. Holmes, R. Pandharipande, R. Schwarz)
Acta Mathematica, 230.2 (2023) - preprint, journal version
- 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)**
SIAM J. Discrete Math (SIDMA), 37.2 (2023) - journal version
- 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)
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
Links
Theses
Talks
- Conjectural relation of moduli spaces of twisted \(k\)-differentials and Pixton's class, ETH Zurich, 2017
- PhD defense talk, ETH Zurich, 2019
- The relation between strata of k-differentials and double ramification cycles (version 2), Algebraic Geometry and Moduli Zoominar, 2020
- Interactive talk on admcycles, Algebraic Geometry and Moduli Zoominar, 2020
- Another interactive talk on admcycles, Leiden, 2020
- Intersection numbers of psi-classes with strata of k-differentials and double ramification cycles, Oberwolfach, 2021
- Logarithmic double ramification cycles, Stony Brook, 2022
- A logarithmic approach to spaces of multi-scale differentials, Frankfurt, 2023
- Using computer algebra to study intersection theory of moduli spaces, Les Diablerets, 2023 (CoCalC link)
- Logarithmic intersection theory - from toric varieties to moduli of curves, lecture series, Zurich, 2023
Posters
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