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.

MAT016 - Proofs from The Book (Spring term 2023)

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

• 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)
  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

• 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

• 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).

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)