Tropical combinatorics and Ehrhart theory

From CRCG-Wiki

We study combinatorial questions on the intersection of the tropical hypersurfaces defined by tropical polynomials $g_1, ..., g_k$ in $n$ variables with Newton polytopes $P_1, \ldots, P_k$, such as the $f$-vector, the number of unbounded faces and (in case of a curve) the genus. In particular, by establishing some aspects of a mixed Ehrhart theory we show that the genus of a tropical intersection curve equals the genus of a toric intersection curve corresponding to the same Newton polytopes. (Based on joint work with Reinhard Steffens, arXiv:0902.1072)