/ 5月 27, 2011/ 静岡代数学セミナー

(+ := @ipc.shizuoka.ac.jp)

その場合，1コマ目に遅刻する可能性があれば，事前に連絡しておいてもらった方が無難です．
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プログラム

05月27日（金）

13:45 – 14:45 Grant, Joseph（名古屋大学多元数理）
Representations, derived categories, and autoequivalences, I

15:00 – 16:00 Grant, Joseph（名古屋大学多元数理）
Representations, derived categories, and autoequivalences, II

16:15 – 17:15 毛利 出（静岡大学理）
McKay correspondence for iterated Ore extensions

18:30 – 懇親会

05月28日（土）

10:00 – 11:30 栗林 勝彦（信州大学理）
Gorenstein spaces and derived string topology

11:45 – 12:45 谷本 龍二（静岡大学教育）
$\mathbb{G}_a$の計算不変式論

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• Grant, Joseph
Representations, derived categories, and autoequivalences
Representations, derived categories, and autoequivalences: I will discuss representations of symmetric algebras and Calabi-Yau properties. Then I will present a method to construct symmetries of derived categories, based on periodic algebras, which is related to the spherical twists of Seidel and Thomas. Finally I will give some examples of this construction.
• 毛利 出
McKay correspondence for iterated Ore extensions
McKay correspondence for iterated Ore extensions: The classical McKay correspondence is a correspondence between the minimal resolution of the affine scheme associated to the fixed subalgebra of the polynomial algebra in two variables by a finite subgroup of the special linear group of degree 2 and the preprojective algebra of the McKay quiver of that group. In this talk, we will see that there is a similar correspondence in the case that a finite cyclic subgroup of the general linear group of degree n acts on an n-th iterated Ore extension of the field, which is a noncommutative deformation of the polynomial algebra in n variables. This is a survey talk. We will try to give most of the basic definitions and explain the results by simple examples.

• 栗林 勝彦
Gorenstein spaces and derived string topology
Gorenstein spaces and derived string topology: String topology of Chas and Sullivan describes a rich structure in the homology of the free loop space of a closed oriented manifold. The most basic operation is an intersection type product on the shifted homology. Recently, the product is generalized to so called string (TQFT) operations by Cohen and Godin. The key step to defining these operations is to construct wrong way maps on the homology of manifolds. In this talk I will give a brief overview of Gorenstein spaces, which is no longer a manifold in general, and discuss wrong way maps on the spaces with a remarkable result due to Felix and Thomas. The setting enables us to deal with string topology in the derived category of differential graded modules over the singular cochain algebra of a Gorenstein space. If time permits, I will go on to describe the dual to loop (co)products in terms of the torsion functors.
• 谷本 龍二
$\mathbb{G}_a$の計算不変式論
$\mathbb{G}_a$の計算不変式論: 不変式環の生成系を記述することは，不変式環の構造決定に向け，基本的である．$\mathbb{G}_a$による不変式論における難所は次にある．ヒルベルトの第１４問題に対する反例に見られるように，$\mathbb{G}_a$による不変式環は必ずしも有限生成とは限らない．また，たとえ$\mathbb{G}_a$不変式環が有限生成であったとしても，生成系の記述は一般に難しい．本講演では，$\mathbb{G}_a$不変式環が有限生成であるとき，生成系を出力するアルゴリズムについて述べる．なお，$\mathbb{G}_a$不変式論の基本的用語である，locally finite iterative higher derivationや，局所スライスなどについても簡単に紹介する．