I am broadly interested in the geometry, topology, and arithmetic of algebraic varieties, with a focus on the development and application of combinatorial methods in algebraic geometry, especially through connections to tropical and nonarchimedean analytic geometry. My work is partially supported by NSF DMS–1068689 and NSF CAREER DMS–1149054.
My teaching in 2013–2014 will include two semesters of algebraic geometry at the graduate level and a spring section of second semester calculus (MATH 115).
I also serve as the faculty sponsor for Yale Splash, on the scientific committee of GAeL, on the organizing committee for AGNES, and sponsor undergraduate research projects throughout the year.
Together with Asher Auel, Dustin Cartwright, and Dave Jensen, I run a weekly seminar on algebraic and tropical geometry. We meet on Thursday afternoons, 4:30–5:30 pm, in 431 DL.
Specialization of Linear Series for Tropical and Algebraic Curves, Banff International Resesarch Station (co-organized with Matt Baker, Lucia Caporaso, Angie Cueto, and Eric Katz). March 30–April 4, 2014.
Tropical and Nonarchimedean Analytic Geometry, AMS
Mathematical Research Communities workshop at Snowbird (co-organized with Matt Baker). June 9–15, 2013.
Algebraic Geometry NorthEastern Series (AGNES), Yale University (co-organized with Mikhail Kapranov). April 19–21, 2013.
Nonarchimedean and Tropical Geometry, Simons Symposium (co-organized with Matt Baker). March 31–April 6, 2013. Notes from talks.
Slides and videos from selected talks
Topology of nonarchimedean analytic spaces. Current Events Bulletin. AMS/MAA Joint Meetings, San Diego. January 11, 2013.
Limits of tropicalizations. Special Session on Tropical Geometry. AMS/MAA Joint Meetings, San Diego. January 9, 2013.
Bidding Games. Department Colloquium, Eindhoven. May 30, 2012.
Tropical and nonarchimedean analytic geometry of curves. Latin School of Algebraic Geometry (ELGA), Córdoba, Argentina. August 11, 2011.
Nonarchimedean geometry, tropicalization, and metrics on curves. AGNES Spring 2011, MIT. April 25, 2011.
Boundary complexes of varieties. MSRI conference on Combinatorial, Enumerative, and Toric Geometry. March 25, 2009.