University of Prince Edward Island, June 5 - 8, 2015
The theory of Newton-Okounkov bodies is a generalization of the rich
theory of toric varieties; it associates a convex body to an arbitrary variety
(equipped with auxiliary data). Although initial steps have been taken for
formulating geometric situations under which the Newton-Okounkov body is a
rational polytope, there is much that is still unknown. In particular,
very few concrete and explicit examples have been computed thus far.
During my graduate studies I have been working on explicitly computing
Newton-Okounkov bodies of Peterson and Bott-Samelson varieties. These
varieties arise, for instance, in the geometric study of representation
theory. In this introductory level talk, I plan to motivate why this theory is important.