Eric Katz (mathematician)

Eric Edward Katz (born circa 1977) is an American mathematician .

biography

Katz graduated from Ohio State University with a bachelor's degree in 1999 and received his doctorate from Stanford University under Yakov Eliashberg (A Formalism for Relative Gromov-Witten Invariants) in 2004 . As a post-doctoral student , he was Assistant Research Professor at Duke University (until 2007), at the University of Texas at Austin and at MSRI (2009). In 2011 he became an Assistant Professor at the University of Waterloo (and an Associate Professor in 2016) and an Assistant Professor at Ohio State University in 2016.

He deals with combinatorial and algebraic geometry. With June Huh he proved a special case of the Rota conjecture, which says that the coefficients of the chromatic polynomial of a matroid form a log-concave sequence (that is, ). Katz succeeded in proving the general Rota conjecture in a joint work with Adiprasito and Huh in 2015 by connecting it to Hodge-Riemann relations of matroids. ${\ displaystyle a_ {i + 1} a_ {i-1} \ leq a_ {i} ^ {2}}$

An Algebraic Formulation of Symplectic Field Theory. Journal of Symplectic Geometry, Volume 5, 2007, pp. 385-437
with June Huh: Log-concavity of characteristic polynomials and the Bergman fan of matroids, Mathematische Annalen, Volume 354, 2012, pp. 1103-1116. Arxiv
with Adiprasito, Huh: Hodge theory of matroids, Notices AMS, Volume 64, January 2017, pp. 26-30, pdf
with Karim Adiprasito, June Huh: Hodge theory for combinatorial geometries, Annals of Mathematics, 2018, Arxiv
What is tropical geometry?, Notices of the AMS, April 2017
with Joseph Rabinoff, David Zureick-Brown: Uniform bounds for the number of rational points on curves of small Mordell-Weil rank, Duke Mathematical Journal, Volume 165, 2016, pp. 3189-3240.

Matthew Baker: Hodge theory in combinatorics, Bulletin of the American Mathematical Society, Volume 55, 2018, pp. 57-80, online