Assistant Professor, Florida State University
Office: LOV 109
Mailing Address: 208 Love Building, 1017 Academic Way, Tallahassee, FL 32306-4510
Mathematical interests: My primary interest is in non-Archimedean geometry and its interactions with the tropical and birational geometry of algebraic varieties. I also like to think asymptotics in algebraic varieties over finite fields, and about operads, especially in the context of algebraic geometry.
Education: I received my Ph.D. from Yale University, under the direction of Mikhail Kapranov, and I did my undergraduate work at the University of California, Berkeley.
Publications and preprints
∎ with Max Hully. Rank-2 tropical deformations. (in preparation)
∎ with Sam Payne. Limits of tropicalizations II: structure sheaves, adic spaces and cofinality of Gubler models. (in preparation)
∎ with Efrat Bank. Correlations between primes in short intervals on curves over finite fields. arXiv: 1708.07491, August 2017. (submitted for publication)
∎ with Joseph Rabinoff, Farbod Shokrieh, and Alejandro Soto. Non-Archimedean and tropical theta functions. arXiv: 1705.08212, May 2017. (submitted for publication)
∎ Galois actions on analytifications and tropicalizations. arXiv: 1703.07593, March 2017. (submitted for publication)
∎ with Efrat Bank. Primes in short intervals on curves over finite fields. arXiv: 1701.06822, January 2017. (submitted for publication)
∎ with Dhruv Ranganathan, Mattia Talpo, and Martin Ulirsch. Logarithmic Picard groups, chip firing, and the combinatorial rank. arXiv: 1611.10233, November 2016.(submitted for publication)
∎ with Dhruv Ranganathan. Degenerations of toric varieties over valuation rings. Bull. Lond. Math. Soc. 48 (2016), no. 5, 835–847.
∎ Introduction to adic tropicalization. Nonarchimedean and Tropical Geometry (Matthew Baker and Sam Payne, eds.). Simons Symposia, Springer New York, 2016, pp. 337-364
∎ with Po Hu and Igor Kriz. D-structures and derived koszul duality for unital operad algebras. J. Pure Appl. Algebra 220 (2016), no. 3, 1133–1156.
∎ with Dhruv Ranganathan. Hahn analytification and connectivity of higher rank tropical varieties. Manuscripta Math. 151 (2016), no. 3-4, 353–374.
∎ with Morgan Brown. Rational connectivity and analytic contractibility. Journal fu ̈r die reine und angewandte Mathematik (to appear)
∎ Higher configuration operads in algebraic geometry: By way of quiver Grassmannians. ProQuest LLC, Ann Arbor, MI, 2013. Thesis (Ph.D.) ⎯ Yale University.
∎ Higher configuration operads by way of quiver Grassmannians. arXiv: 1211.4525, November 2012.
∎ with Philipp Gross and Sam Payne. Limits of tropicalizations. Israel J. Math., 201(2):835-846, 2014.
∎ A noncommutative version of the natural numbers. arXiv: 1003.2081, March 2010.