Category:代数セミナー
数学特別セミナー: 津野祐司 氏 (12月6日)
場所: 自然系学系棟D814セミナー室
講演者: 津野祐司 氏 (千葉工大)
タイトル: 自由ホップ代数に対するクレフト拡大の自明性について
概要:
ホップガロア拡大とは,代数幾何学における群スキームに対する主等質空間(torsor)の非可換版と考えられます.さらに正規底をもつホップガロア拡大,または同値な条件として,ホップ代数の2-コサイクルを用いた接合積によって記述される環の拡大をクレフト拡大と呼びます.本講演では,「竹内光弘氏によって構成された, 勝手な余代数C によって生成される自由ホップ代数をH(C) で表すとき, H(C)-クレフト拡大は自明なものに限るか」という問題に対して,
(i) C が余可換の場合,
(ii) C の余根基が余可換の場合(この場合, 基礎可換環を体とする),
(iii) C が n×n 行列余代数の場合
に得られた結果をご紹介します. 時間があればH(C) のquasi-freeness (代数幾何学におけるformal smoothness の非可換版)にも触れ,その応用についてもお話したいと考えております.
多くの方々のご来聴をお待ちしています.
世話人 増岡彰
代数特別セミナー (11月15日)
場所: 自然系学系棟 D509
タイトル: Higher Chow cycles on Abelian surfaces
講演者: Ramesh Sreekantan 氏 (The Indian Statistical Institute in Bangalore)
概要:
In this talk we use generalizations of beautiful classical geometric constructions of Kummer and Humbert to construct new higher Chow cycles on Abelian surfaces and K3 surfaces over p-adic local fields, generalising some work of Collino. The existence of these cycles is predicted by the poles of the local L-factor at p of the L-function of the Abelian surface. The techniques involve using some recent work of Bogomolov-Hassett and Tschinkel on the deformations of rational curves on K3 surfaces.
代数分野:特別セミナー (11月1日)
代数分野:特別セミナー
日時 11月1日木曜 15:15-16:30
ColorSymmetries Associated with Non-Periodic Structures
Ma. Louise Antonette N. De Las Peñas, PhD
Professor, Mathematics Department
Ateneo De Manila University Philippines
With the discovery of quasicrystals in 1984, the research field ofnon-periodic crystallography has grown and expanded in several directions.Structural problems continue to interest mathematicians and physicists.
In this talk, we discuss a method that allows the investigation of symmetriesof non-periodic structures via colorings of cyclotomic integers. In particular,our work looks at ideal colorings of Mn= Z[xn] where xn = e2pi/nis a primitive nth root ofunity for values of n for which Z[xn] is aprincipalideal domain and thus has class number one. The values of n are groupedinto classes with equal value of f(n),the Euler’s totient function. In the lecture, some results on color groups andcolor preserving groups will be presented.
The colorings of Mn may be manifested geometricallyas a vertex or tile coloring of a two dimensional tiling with n-foldrotational symmetry, which is non-periodic for f(n) > 2. For suchcases, since Mn is dense on the plane, we choose a discretesubset of Mn for which we show the colors. The discovery ofquasiperiodic tilings such as the Penrose tiling, also raised the questionabout color symmetries of such tilings.
群論を応用して複数の分子からなる結晶構造を調べる研究のお話です。
連絡先 秋山茂樹(4395)
代数特別セミナーのお知らせ (8月27日)
以下のように代数特別セミナーを開催いたします。
多くの皆様のご来聴お待ちしております。
日時: 8月27日(月) 16:15-17:30
場所: 自然系学系棟D814 セミナー室
講師: 山根宏之先生(大阪大学)
講演題: 一般化された量子群のハリス・チャンドラ型定理
講演概要:一般化された量子群の中心の構造をあきらかにするハリス・チャンドラ型定理を,
私が以前Heckenbergerと求めたシャポバロフ行列式の因数分解をもちいて
Kac-Kazhdanの手法で証明します. これはPunita Batraとの共同研究です.
世話人 増岡彰(4368)
(代理投稿 川村一宏)
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