Research

I am broadly interested in the geometry, topology, and arithmetic of algebraic varieties. My research focuses on the development and application of combinatorial methods in algebraic geometry, especially through the application of tropical and nonarchimedean analytic techniques. This work is partially supported by NSF DMS-1068689 and NSF CAREER DMS-1149054.

Professional Activity

I am currently an assistant professor in the Department of Mathematics at Yale Univeristy and serve as a faculty sponsor for Yale Splash, on the scientific committee of GAeL, and on the organizing committee for AGNES, which will take place at Yale on April 19-21, 2013. For details and registration, please visit the workshop homepage. The registration deadline is March 15.

Matt Baker and I are organizing two upcoming workshops on tropical and nonarchimedean analytic geometry, a Simons Symposium in April 2013, and an AMS Mathematical Research Communities program at Snowbird, on June 9-15, 2013. Further details and application instructions for the MRC program are available here. The application deadline is March 1.

If you are interested in research in tropical geometry and related fields, you will find people to talk with at Yale, including Professors Alexander Goncharov and Mikhail Kapranov, NSF Postdoctoral Fellow and Gibbs Assistant Professor Dustin Cartwright, and PhD students Soumya Banerjee, Tyler Foster, Yoav Len, and Linhui Shen. Dustin Cartwright and I are also organizing a seminar on algebraic and tropical geometry, Thursdays at 4:30 pm, in 431 DL.

I am currently co-teaching a graduate course on Polytopes, Toric Varieties, and Tropical Geometry, with Gil Kalai. Office hours are by appointment, in 414 DL.

Slides and videos from recent 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.

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