MathCCSセミナー 2024/10/28

日時 / Date

2024年10月28日（月）15:00～17:30 / October 28th (Mon) 2024 15:00–17:30

場所 / Venue

AIMR本館 5階コンビネーションルーム / Combination Room, 5th floor, AIMR Main Building

Speaker 1

山田 裕史（岡山大学）/ HiroFumi Yamada (Okayama University)

Title

Combinatorics of the KdV equation

Abstract

Korteweg-de Vries (KdV) equation describes the nonlinear waves of the shallow water : u_{t} = u_{xxx} + 6uu_{x}.
Around 45 years ago, Mikio Sato established a general theory for this kind of soliton equations. Although Sato’s theory is a splendid algebraic analysis, some tiny combinatorics escaped from the main stream. In the talk I will try to glean those combinatorial aspects from the viewpoint of representation of the symmetric groups.

Speaker 2

藤田 直樹（熊本大学）/ Naoki Fujita (Kumamoto University)

Title

Schubert calculus on convex polytopes and semi-toric degenerations

Abstract

A goal of Schubert calculus is to compute the structure constants of the cohomology ring of a flag variety with respect to the basis consisting of Schubert classes. One approach to such computation is to realize Schubert classes as concrete combinatorial models such as Schubert polynomials. In this talk, we discuss a combinatorial model of Schubert calculus using convex polytopes such as Newton-Okounkov polytopes. Newton-Okounkov polytopes of flag varieties arising from their cluster variety structure induce degenerations of Schubert varieties into unions of irreducible toric varieties, called semi-toric degenerations. Such semi-toric degenerations can be expected as combinatorial models of Schubert classes.

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本セミナーはAIMR数学連携グループとの共催です。