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.

401-3146-12L - Algebraic Geometry (Spring term 2024)

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

• k-leaky double Hurwitz descendants (joint with R. Cavalieri, H. Markwig)
  Preprint (2024) - preprint
• Birational classification of toric orbifolds
  European Journal of Mathematics, 10. (2024) - preprint, journal version
• 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

• 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

• Hausdorff school “Perverse Sheaves in Enumerative Geometry” (February 10-14, 2020).
• Online working seminar “Smooth compactifications and bChow intersections via blowups/subdivisions” (Summer 2020).
• Workshop admcycles: coding intersection theory (Spring 2022).
• Workshop Moduli spaces: theory and coding

• Not who you are looking for? Maybe you should try the other Johannes Schmitt working on (computational) algebraic geometry!
• A guide on how to get started using SageMath

• 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

• 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

• Moduli spaces of self-maps of \(\mathbb{CP}^1\), AMS Summer Institute 2015, Salt Lake City
• Twisted \(k\)-differentials, GAeL-conference 2017, Bath