日 時： 2016年7月8日（金）, 9日（土）
場 所： 静岡大学理学部 C 棟 309 号室
案 内： http://www.shizuoka.ac.jp/access/index.html
理学部 A 棟1階から入り，エレベーターで4階まで上がり，渡り廊下を渡ると，理学部 C 棟の1階に着きます．
連絡： 浅芝秀人 (shasash+), 毛利出 (mori.izuru+),
(+ := @ipc.shizuoka.ac.jp)
注意： 土曜日，理学部棟は施錠されています。
鍵を開けるため9時すぎから9時半近くまでA棟1階の入り口に人員を配置します。
1日だけの参加も大歓迎です。
その場合，土日の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
7月8日（金）
13:30 – 14:30 石塚裕大（京都大学大学院理学研究科）
Arithmetic of linear determinantal representations, I
14:45 – 15:45 Aaron Chan（Uppsala, 名古屋大学多元数理）
Elementary examples of categorifications and introduction to representations of (multi)semigroups
16:00 – 17:00 Razieh Vahed（IPM-Isfahan, 静岡大理）
Derived equivalences of functor categories
18:30 – 懇親会
12月19日（土）
09:30 – 10:30 Rasool Hafezi（IPM-Isfahan, 静岡大理）
On Auslander’s Formula
10:45 – 11:45 石塚裕大（京都大学大学院理学研究科）
Arithmetic of linear determinantal representations, II
13:30 – 14:30 Aaron Chan（Uppsala, 名古屋大学多元数理）
On a 2-representation theory of 2-categories
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アブストラクト
- 石塚裕大：Arithmetic of linear determinantal representations, I, II
行列式表示は、超曲面の定義方程式を適切な形の行列式によって表示できるかという疑問である。その素朴さゆえに、150年前の Hesse の研究に始まって、さまざまな視点から再発見されてきたテーマでもある。今回の講演では、自身の結果、および伊藤哲史氏との共同研究を主軸として、特に数論的な設定における行列式表示について知られている事実や、背景にある考え方を紹介する。
- Aaron Chan：1. Elementary examples of categorifications and introduction to representations of (multi)semigroups
Categorification often gives surprising results to mathematics, yet its essential philosophy is a counter-intuitive one – we gain insight by complicating mathematical structures! Some elementary examples will be shown in this talk. I will then move on to giving a crash course on the representation theory of (multi)semigroups. This serves as foundation material for the second talk, but can also be of independent interest to general algebraists.
2. On a 2-representation theory of 2-categories
In a series of works initiated by Mazorchuk and Miemietz, they introduced a “2-representation theory of 2-categories” by formalising the categorification of Kazhdan-Lusztig theory and of semigroup representations (arXiv: 1011.3322, 1112.4949, 1207.6236, 1304.4698, 1404.7589, 1408.6102). The goal of the second talk is to provide some aid for representation theorists on reading this stream of works. I will introduce the definitions, notions, and results used in these papers by sticking to one example – the categorification of the symmetric gorup of order 2. If time allows, I will briefly survey various developments in this theory.
- Razieh Vahed：Derived equivalences of functor categories
Tilting theory is initiated from representation theory of nite dimensional algebras, with origins in the work of Bernstein, Gel’fand and Ponomarev. It is known that tilting theory can be viewed as a generalization of classical Morita theory. In this direction, one of the most beautiful results is the Rickard’s theorem that characterizes all rings that are derived equivalent to a given ring A by determining all tilting complexes over A . On the other hand, functor categories were introduced in representation theory by Auslander. He used this kind of categories to classify artin algebras of finite representation type as well as to prove the first Brauer-Thrall conjecture. Let Mod-S denote the category of S -modules, where S is a small category. In this talk, we provide a version of Rickard’s theorem on derived equivalence of rings for Mod-S. This will have several interesting applications. This talk is based on a joint work with J. Asadollahi and R. Hafezi.
- Rasool Hafezi：On Auslander’s Formula
Auslander’s Formula was discovered in 1960s. This formula suggests that one way of studying a abelian category is to study the category of all finitely presented functors from given abelian category to the category of abelian groups which has nicer homological properties. In my talk, some different versions of this formula will be explained. Then I will give some applications of our results for artin algebras.