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# 代数特別セミナーのお知らせ(7月19日)

以下のように代数特別セミナーを開催します。皆様のお越しをお待ちしております。

木村健一郎先生代理

川村一宏

日時： 7月19日(木) 15:00 － 17:15

場所: 自然系学系 D棟 509号室

講演1

時間: 15:00～16:00

講演者: Noriko Yui (Queen's University)

タイトル： Modularity (automorphy) of Calabi-Yau varieties over Q

概要: I will present the current status on the modularity

of Calabi-Yau varieties defined over the field of rational numbers.

Here modularity is in the sense of the Langlands Program. In the first part,

I will formulate the modularity conjectures for Calabi-Yau varieties of

dimension 1, 2 and 3, and discuss the recent modularity results. If there

is time, I will report on the recent joint wotrk with Y. Goto and R. Livne on

automorphy of certain K3-fibered Calabi-Yau threefolds, and mirror symmetry.

講演２：

時間: 16:15～17:15

講演者: George Elliott (University of Toronto)

タイトル: A brief history of non-smooth classification theory

概要：It was first within the theory of C*-algebras thatit was noticed---by Mackey

(or at least suspected by him!)---that the classification up to isomorphism of

a well-behavedensemble of objects (nicely parametrized)---in this case,

the irreducible representations of a given C*-algebra---might beno longer well behaved,

the corresponding quotient space of the"standard" Borel space of given objects

possibly being decidedlynonstandard (much like the real numbers

modulo the subgroup ofrationals).Interestingly, perhaps, it was also first

within the theoryof C*-algebras that this problem was circumvented

in a non-trivialway---by passing from the given category of objects

to a new categoryin an invariant way (by means of a functor), in such a way that

the new category is also well-behaved (e.g., a standard Borelspace), so

it is not just the set of isomorphism classes of theoriginal objects

(which would be non-smooth), but is still asimpler category than the original one---

for the simple reasonthat all inner automorphisms (if not all automorphisms) become

trivial. The first example of this was discovered by Glimm andDixmier, and

enlarged on later by Bratteli and Elliott---it was,incidentally, also work of Glimm

that confirmed Mackey'sdiscovery. This functorial treatment of a non-smooth

classification setting (isomorphism within a certain classof C*-algebras) was

the first use of K-theory in operatoralgebras. (Not counting the Murray-von Neumann type

classification of von Neumann algebras!)

問い合わせ先: 木村健一郎