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 1 October, 2014
10月23日（木）16:30 -18:00, 第二校舎6号館6718
原田 芽ぐみ 氏（McMaster University & 大阪市立大学）
Newton-Okounkov bodies, representation theory, and Bott-Samelson varieties
概要:
The theory of Newton-Okounkov bodies is a far-reaching generalization of the theory of toric varieties. In particular, it can associate to any complex projective variety X a convex body (which is a rational polytope in many cases) of dimension equal to the complex dimension of X; in the case when X is a toric variety, the convex body is exactly the usual Newton polytope. Moreover, in a recent paper, Kaveh showed that the string polytopes in geometric representation theory are special cases of Newton-Okounkov bodies associated to flag varieties G/B. Hence the theory of Newton-Okounkov bodies is naturally related to many interesting questions in representation theory and Schubert calculus. The Bott-Samelson varieties give resolutions of singularities of Schubert varieties and are central in the study of the geometry of G/B. I will give an overview of this subject in relation to Newton-Okounkov bodies and discuss some recent and ongoing work, as well as some open questions.
5月14日（水）16:30 -18:00, 第二校舎6号館6718
窪田 陽介 氏（東大数理）
The joint spectral flow and localization of the indices of elliptic operators
概要:
The joint spectral flow is a generalization of the spectral flow for n-parameter families of mutually commuting n-tuples of self-adjoint operators. Its precise definition is given in terms of Segal's model of the connective K-theory spectrum. I will explain an application of it for some localization results of indices, motivated by Witten's deformation of Dirac operators.
参考文献：
- G. Segal. K-homology theory and algebraic K-theory. In K-theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975), pp. 113-127. Lecture Notes in Math., Vol. 575. Springer, Berlin, 1977.
2013年度の幾何セミナーの記録