I am a postdoc at ETH Zurich working in algebraic geometry, under Rahul Pandharipande . My advisor was Dan Abramovich .
Other Information
My CVMy 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 |
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| 2. | Localization for Logarithmic Stable Maps joint with E. Routis - in Transactions of the American Mathematical Society, Series B, 6 (2019) |
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| 3. | Logarithmic Stable Toric Varieties and Their Moduli joint with K. Ascher - in Algebraic Geometry 3(2016), no. 3, 296-319 |
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| 4. | Moduli of Morphisms of Logarithmic Schemes Appendix C in J. Wise's paper - in Algebra Number Theory 10 (2016), no.4, 695-735 |
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| 5. | A Theory of Stacky Fans with W.D. Gillam |
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| 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. |
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| 8. | Logarithmically Regular Maps with M. Temkin - in Math Ann. 379 (2021), no. 1-2, 325-346 |
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| 9. | Models of Jacobians of Curves joint with D. Holmes, G. Orrechia, T. Poiret |
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| 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 |
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| 11. | A case study of intersections on blowups of the moduli of curves joint with D. Ranganathan |
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| 12. | Tropicalization of the universal Jacobian joint with M.Melo, M. Ulirsch, F. Viviani - in Épijournal de Géométrie Algébrique, Volume 6 (2022) |
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| 13. | Logarithmic Double Ramification Cycles joint with D.Holmes, R.Pandharipande, A. Pixton, J. Schmitt |
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| 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 |
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| 17. | Tropicalizing the Moduli Space of Broken Toric Varieties joint with J. Wise |
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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 |