Tyler Foster

Assistant Professor, Florida State University

Email: tsfoster[at]math[dot]fsu[dot]edu

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.

Teaching: This Fall 2018 semester, I am teaching Calculus III (MAC2313, Section 0010).

If you are enrolled in the course, you can access our course website at https://canvas.fsu.edu/courses/62227.

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.