Research Focus
I am interested in non-Archimedean analytic and tropical geometry, combinatorics, algebraic and arithmetic geometry,
Publications
- The monodromy pairing and discrete logarithm on the Jacobian of finite graphs. Journal of Mathematical Cryptology, Volume 4, Issue 1, Pages 43-56, 2010.
- Chip-firing games, potential theory on graphs, and spanning trees. Journal of Combinatorial Theory, Series A, Volume 120, Issue 1, Pages 164-182, 2013. (with Matthew Baker)
- Divisors on graphs, connected flags, and syzygies. International Mathematics Research Notices (IMRN), no. 24, Pages 6839-6905, 2014. (with Fatemeh Mohammadi)
- Canonical representatives for divisor classes on tropical curves and the Matrix-Tree Theorem. Forum of Mathematics, Sigma, Volume 2, 25 pages, 2014. (with Yang An, Matthew Baker, and Greg Kuperberg)
- Divisors on graphs, binomial and monomial ideals, and cellular resolutions. Mathematische Zeitschrift, Volume 283, Issue 1, Pages 59-102, 2016. (with Fatemeh Mohammadi)
- Non-Archimedean and tropical theta functions. Mathematische Annalen, Volume 372, Issue 3-4, Pages 891-914, 2018. (with Tyler Foster, Joseph Rabinoff, and Alejandro Soto)
- Canonical measures on metric graphs and a Kazhdan's theorem. Inventiones mathematicae, Volume 215, Issue 3, Pages 819-862, 2019. (with Chenxi Wu)
- Limits of canonical forms on towers of Riemann surfaces. Journal für die reine und
angewandte Mathematik, 2019. DOI 10.1515/crelle-2019-0007. (with Hyungryul Baik and Chenxi Wu) - Effective divisor classes on metric graphs. 29 pages, 2018. (with Andreas Gross and Lilla Tóthmérész)
- Metric graphs, cross ratios, and Rayleigh's laws. 24 pages, 2018. (with Robin de Jong)
- Tropical moments of tropical Jacobians. 34 pages, 2018. (with Robin de Jong)
- Faltings height and Néron-Tate height of a theta divisor. 31 pages, 2018. (with Robin de Jong)
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A sheaf-theoretic approach to tropical homology, 56 pages, 2019. (with Andreas Gross)
