Speaker

藤田直樹 (東京大学大学院数理科学研究科)

Date

October 8, 11:00-11:50

Title

Combinatorial mutations on representation-theoretic polytopes (slide)

Abstract

A Newton-Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gives a systematic method of constructing toric degenerations of projective varieties. Its combinatorial properties heavily depend on the choice of a valuation, and it is a fundamental problem to relate Newton-Okounkov bodies associated with different kinds of valuations. In this talk, we address this problem for flag varieties using the framework of combinatorial mutations which was introduced in the context of mirror symmetry for Fano varieties. By applying sequences of combinatorial mutations, we connect Newton-Okounkov bodies of flag varieties arising from representation theory and cluster theory, which include string polytopes, Nakashima-Zelevinsky polytopes, and FFLV polytopes. This is joint work with Akihiro Higashitani.