日 時： 2008年12月5日（金）, 6日（土）
場 所： 静岡大学理学部 C 棟 309 号室
案 内： http://www.shizuoka.ac.jp/ippan/shizuoka.html
連絡：浅芝秀人 (shasash+)，毛利出 (simouri+)
(+ := @ipc.shizuoka.ac.jp)
プログラム（暫定的）
12月5日（金）
14:00-15:00 浅芝 秀人（静岡大学） “Cluster categories are not orbit categories”
15:20-16:20 服部 陽一（東京大学） “Noncommutative projective schemes associated to quantum affine coordinate rings which are birationally equivalent but not Morita equivalent”
16:40-17:40 Oeyvind Solberg（ノルウェー工科大学 (NTNU in Trondheim)） “(Sub-)additive functions and support varieties”
18:30-20:30 懇親会
12月6日（土）
前日の講演のより詳しい内容や質問討論からなります． 時間の大体の目安は，
1コマ目：09:00-10:30
2コマ目：11:00-12:30
土曜日だけの参加も可能ですが，その場合は事前にご連絡ください． （土曜日，理学部棟は施錠されています．）
要約
- Asashiba
(1) We fix a commutative ring k and assume all categories and functors are k-linear. Suppose that an action of a group G on a category C is given by a monomorphism G –> Aut(C) (:= the group of automorphsms of C). Then an orbit category C/G is defined. On the other hand suppose that a category C’ is G-graded. Then a smash product C’#G is defined. We show that there is a weakly G-equivariant equivalence C –> (C/G)#G of categories with G-actions (note that the G-action on C is not always free, whereas the G-action on (C/G)#G is always free) and that there is a homogeneous equivalence C’ –> (C’#G)/G of G-graded categories. (2) We also show that the pullup functor and pushdown functor of the canonical G-covering functor C –> C/G induce equivalences Mod C/G –> Mod^{G} C (:= the category of G-invariant C-modules) and Mod C –> Mod_{G} C/G (:= the category of G-graded C/G-modules) even when the G-action on C is not necessarily free. (3) When G = is an infinite cyclic group and the action of g on C is defined by an autoequivalence of C modulo natural isomorphisms, an orbit category C/G should be defined as C/G:= (ZC)/G by replacing C by a larger category ZC such that the action of g on ZC is given by an automorphism of ZC. We show that there is a category C_{g} such that ZC is given by a smash product ZC = C_{g} # G. Then we see that C/G = (C_{g}#G)/G is equivalent to C_{g} as G-graded categories. Thus we can say that C/G is not an orbit category but just the category C_{g}. Cluster categories or root categories are examples of this construction. - Hattori
When studying about noncommutative projective schemes, we usually consider one induced from A.S-regular algebras. Quantum affine coordinate ring is the most basic object in this class. I will show an example which is particular to over 4-dimension. - Solberg
The representation theory of finite dimensional algebras have a side that is of combinatorial nature. One such instance is the use of sub-additive and additive functions on graphs. On the other hand, the theory of support varieties provide an example of a link between algebraic geometry and representation theory. This lecture has as an aim to show how all these notions are used together to give information about the possible shapes of the stable components of the Auslander-Reiten quiver. The talk will begin with reviewing the definitions and some results about sub-additive and additive functions on graphs. Then the necessary background and results on support varieties will be explained. Next we describe a link between (sub-)additive functions and components of the stable Auslander-Reiten quiver, and how support varieties induce such functions on the three class of the components. If time premits, we give new classes of algebras where the theory of support varieties applies.