幾何学セミナー

場所：明治大学生田キャンパス
世話係：吉田尚彦


Last updated 19 October 2017
12月18日（月）17:10 -18:50， 第二校舎6号館6718

二木 昌宏 氏（千葉大学）

Gluing cotngent bundles and the Hochschild cohomology of wrapped Fukaya categories

概要: In 2001 Cieliebak proved that the symplectic cohomology remains unchanged under the subcritical Weinstein handle attachment. Symplectic cohomology is expected to be isomorphic to the Hochschild cohomology of the wrapped Fukaya category, for which Ganatra established a criterion. I'm going to talk about a study in progress about the behavior of the wrapped Fukaya category under the boundary connected sum, which is a special case of the subcritical handle attachment.

10月6日（金）13:30 -15:10， 第二校舎6号館6706

原田 芽ぐみ 氏（McMaster University／大阪市立大学）

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.

6月19日（月）15:20 -17:00， 第二校舎6号館6706

田中 祐二 氏（大阪大学）

Vafa-Witten invariants for projective surfaces

概要: This is joint work with Richard Thomas, which defines Vafa-Witten invariants for projective surfaces from the moduli space of the Higgs pairs by using virtual C^* localisations; calculates them in examples; and sees (in great amazement) their partition functions match with the modularity predictions by Vafa and Witten more than 20 years ago. I also try to speak about more updates about them.

参考文献：
  1. L. Gottsche and M. Kool, Virtual refinements of the Vafa-Witten formula, arXiv:1703.07196.
  2. Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: stable case, arXiv:1702.08487.
  3. Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, arXiv:1702.08488.
  4. C. Vafa and E. Witten, A strong coupling test of S-duality, Nucl. Phys. B 432 (1994), 484–550.

2016年度の幾何セミナーの記録