[geometry-ml:03096] 明治大学幾何学セミナーのお知らせ

[吉田尚彦]

皆様

今年度，第二回目の明治大学幾何学セミナーを以下の要領で開催致しますのでお知らせ致します．

日程：2017年10月6日（金）13:30-15:10
場所：明治大学生田キャンパス 第二校舎6号館6706

講演者：原田 芽ぐみ氏（McMaster大学／大阪市立大学）

講演題目：The cohomology of abelian Hessenberg varieties and the
Stanley-Stembridge conjecture

概要：The famous Stanley-Stembridge conjecture in combinatorics states that
the chromatic symmetric function of the incomparability graph of a
so-called (3+1)-free poset is e-positive. In this talk, we briefly discuss
this conjecture, and explain how recent work of Shareshian-Wachs,
Brosnan-Chow, among others, makes a rather surprising connection between
this conjecture and the geometry and topology of Hessenberg varieties,
together with a certain symmetric-group representation on the cohomology of
Hessenberg varieties. In particular, it turns out the Stanley-Stembridge
conjecture would follow if it can be proven that the cohomology of regular
semisimple Hessenberg varieties (in Lie type A) are permutation
representations of a certain form. I will then describe joint work with
Martha Precup which proves this statement for the special case of abelian
Hessenberg varieties, the definition of which is inspired by the theory of
abelian ideals in a Lie algebra, as developed by Kostant and Peterson.  Our
proof relies on the incomparability graph of a Hessenberg function and
previous combinatorial results of Stanley, Gasharov, and Shareshian-Wachs,
as well as previous results on the geometry and combinatorics of Hessenberg
varieties of Martha Precup.


興味を持たれそうな方がおられましたら周知してくださいますと幸いです．皆様のご参加をお待ちしております．

幾何セミナーのホームページ：
http://www.isc.meiji.ac.jp/~takahiko/GeometrySeminar/index.html


吉田尚彦
明治大学理工学部数学科
Takahiko Yoshida
Department of Mathematics
School of Science and Technology
Meiji University

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