Samouil Molcho

Email: samouil.molcho (at) math (dot) ethz (dot) ch


I am a postdoc at ETH Zurich working in algebraic geometry, under Rahul Pandharipande . My advisor was Dan Abramovich .

Other Information

My CV
My Research Statement

Research Interests

Logarithmic and Tropical Geometry; Gromov-Witten Theory and Enumerative Geometry; Tautological Ring and Moduli of Curves; Abelian Varieties.

My research focuses on using techniques of logarithmic geometry to understand geometric problems, particularly problems that arise from moduli theory. In the past few years, I have been studying the interactions between compactified Jacobians, moduli spaces of stable maps and the moduli space of curves, and the cycles arising from these interactions.

Papers

1. Logarithmic Geometry and Manifolds with Corners
joint with W.D. Gillam
link
2. Localization for Logarithmic Stable Maps
joint with E. Routis - in Transactions of the American Mathematical Society, Series B, 6 (2019)
link
3. Logarithmic Stable Toric Varieties and Their Moduli
joint with K. Ascher - in Algebraic Geometry 3(2016), no. 3, 296-319
link
4. Moduli of Morphisms of Logarithmic Schemes
Appendix C in J. Wise's paper - in Algebra Number Theory 10 (2016), no.4, 695-735
link
5. A Theory of Stacky Fans
with W.D. Gillam
link
6. Universal Weak Semistable Reduction
in Israel Journal of Math, 242 (2021), no.1, 55-82
link
7. The Logarithmic Picard Group and its Tropicalization
with J. Wise - in Compositio Mathematica, 158(7), 1477-1562.
link
8. Logarithmically Regular Maps
with M. Temkin - in Math Ann. 379 (2021), no. 1-2, 325-346
link
9. Models of Jacobians of Curves
joint with D. Holmes, G. Orrechia, T. Poiret
link
10. The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves
joint with R.Pandharipande and J. Schmitt - Accepted to Compositio
link
11. A case study of intersections on blowups of the moduli of curves
joint with D. Ranganathan
link
12. Tropicalization of the universal Jacobian
joint with M.Melo, M. Ulirsch, F. Viviani - in Épijournal de Géométrie Algébrique, Volume 6 (2022)
link
13. Logarithmic Double Ramification Cycles
joint with D.Holmes, R.Pandharipande, A. Pixton, J. Schmitt
link
14. Smooth Compactifications of the Abel-Jacobi Section
link
15. Pullbacks of Brill-Noether Classes under Abel-Jacobi Sections
link

The following papers are complete, but my collaborators and I had wanted to revisit in the future to make additions. Since a revision has not happened in a while, and the ideas in the papers have been useful to me in other contexts, I post them here in case someone else finds them helpful as well.
16. Stable Logarithmic Maps as Moduli Spaces of Flow Lines
joint with W.D. Gillam
link
17. Tropicalizing the Moduli Space of Broken Toric Varieties
joint with J. Wise
link

Some Notes

These are notes from some online talks given during the pandemic. I imagine there are quite a few errors inside, but I hope the informal presentation is legible and useful.
1. An overview of Logarithmic Stable Maps (at ETH)
2. Logarithmic Geometry (Four Lectures at ETH)
3. Piecewise Polynomials, \lambda_g and the Log Tautological Ring etc. (at ETH)
4. The Logarithmic Tautological Ring (for the MAP conference)
5. The Strict Transform in Log Geometry (at Stanford)
6. Weak Semistable Reduction (for Dan's seminar at ICERM)
7.Four lectures on Logarithmic Double Ramification Cycles from Navid's "Guided Meditations" Seminar: 1,2,3,4