Title: Newton-Okounkov body computations for M_{0,n}-bar
Abstract: Newton-Okounkov bodies (N.O. bodies) are convex sets that encode asymptotic information about sections of line bundles on a projective variety. In this talk, I will discuss the problem of computing N.O. bodies for line bundles on M_{0,n}-bar, the moduli space of stable pointed rational curves. I will describe an algebraic approach for computing N.O. bodies of arbitrary line bundles on M_{0,n}-bar, as well as a more geometric approach that in general produces only subset of the N.O. bodies. In some cases of interest, we conjecture that the geometric approach produces the entire N.O. body. This talk is based on upcoming joint work with Deniz Genlik.