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

My Research Statement (2019)

My research focuses on using techniques of logarithmic geometry to understand geometric problems, particularly problems that arise from moduli theory. Logarithmic geometry is a beautiful theory developed by Fontaine, Illusie and Kato, which lies on the crossroads between algebraic, tropical and Berkovich geometry. One of the guiding principles of logarithmic geometry is that many singular spaces are smooth in the logarithmic context, and can be studied very effectively using a combination of techniques that are straightforward analogues of the techniques used to study smooth spaces in algebraic geometry together with combinatorics. My early interests were in using logarithmic techniques to study degenerate objects in differential geometry, such as manifolds with corners, and on the algebro-geometric side in degenerations of stable maps and enumerative invariants. Recently I have become interested in log abelian varieties -- in particular log Picard varieties. These are a kind of degeneration of abelian varieties that exist in the logarithmic setting, but cannot exist in the world of classical schemes. In a sentence, they are honest algebraic spaces in the category of log schemes. These spaces have rich structure and some striking properties, but their geometry is mysterious and remains still largely undeveloped. My Oberwolfach report on the Log Picard variety can perhaps give a flavor. Currently, with various collaborators, we are trying to use these spaces to study the moduli space of curves from this different perspective.

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 |
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3. | Logarithmic Stable Toric Varieties and Their Moduli joint with K. Ascher |
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4. | Moduli of Morphisms of Logarithmic Schemes Appendix C in J. Wise's paper |
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5. | A Theory of Stacky Fans with W.D. Gillam |
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6. | Universal Weak Semistable Reduction | link |

7. | The Logarithmic Picard Group and its Tropicalization with J. Wise |
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8. | Logarithmically Regular Maps with M. Temkin |
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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 |
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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 |
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13. | Stable Logarithmic Maps as Moduli Spaces of Flow Lines joint with W.D. Gillam |
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14. | Tropicalizing the Moduli Space of Broken Toric Varieties joint with J. Wise |
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1. | The Logarithmic Deligne Pairing joint with M. Ulirsch, J. Wise |

2. | Crepant Resolutions and the Log McKay correspondence joint with G. Liu |