談話会/Colloquium

Title

最近のホッジ加群の理論の進展について

Date

2014年5月21日(水) 16:30〜17:30    (16:00より1階ロビーでtea)

Place

京都大学数理解析研究所 (RIMS) 110号室
(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

齋藤 盛彦 (Morihiko Saito)氏 (京大・数理研)

Abstract

 代数的な場合のホッジ加群の定義というのは非常に複雑すぎてあまり良くわからないという状態が長く続いて来ましたが、最近やっと満足できる簡単な定式化が得られたので、それについて説明したいと思います。最近の応用についても解説する予定ですが、例えば、法関数の零点の定義体、グリフィスの有理積分の一般化、原始形式への応用、などを考えております。

Comment

Title

Double affine Hecke algebras and refined Jones polynomials of torus knots

Date

2014年4月23日(水) 16:30〜17:30    (16:00より105談話室でtea)

Place

京都大学大学院理学研究科3号館110講演室
(Rm110, Building No.3, Faculty of Science, Kyoto University)

Speaker

Ivan Cherednik 氏 (京大・数理研 & UNC at Chapel Hill)

Abstract

 Using Hecke algebras and Verlinde algebras for calculating the Jones and HOMFLYPT polynomials of torus knots is generally well understood, though the explicit formulas attract a lot of attention even for the simplest knots and are used in the theory of A-polynomials as well as in Number Theory. I will define the DAHA-Jones (refined) polynomials of torus knots for any root systems and any weights (practically from scratch). They generalize those based on Quantum Groups, which was checked for types A-C-D by now. In type A, the DAHA-superpolynomials will be introduced, presumably coinciding with the stable Khovanov-Rozansky polynomials for sl(N) and with those obtained via the BPS states in the M5 theory (String Theory). If time permits, type C will be briefly dicussed, including some latest developments in the rank one case.

Comment

Title

Hodge theory and representation theory.

Date

2014年4月16日(水) 16:30〜17:30    (16:00より1階ロビーでtea)

Place

京都大学数理解析研究所 (RIMS) 110号室
(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

Kari Vilonen 氏 (Northwestern University)

Abstract

 Describing the irreducible unitary representations of reductive Lie groups is the major remaining problem in the representation theory of such groups. I shall describe a Hodge-theoretic approach to this problem. As part of our approach I will formulate general conjectures about Hodge modules. This is joint work with Wilfried Schmid.

Comment

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