BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Yasuaki Gyoda (Nagoya University)
DTSTART:20201027T073000Z
DTEND:20201027T090000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/1
DESCRIPTION:Title: Positive cluster complex and tau-tilting complex\nby
Yasuaki Gyoda (Nagoya University) as part of Tokyo-Nagoya Algebra Seminar
\n\n\nAbstract\nIn cluster algebra theory\, cluster complexes are actively
studied as simplicial complexes\, which represent the structure of a seed
and its mutations. In this talk\, I will discuss a certain subcomplex\, c
alled positive cluster complex\, of a cluster complex. This is a subcomple
x whose vertex set consists of all cluster variables except for those in t
he initial seed. I will also introduce another simplicial complex in this
talk - the tau-tilting complex\, which has vertices given by all indecompo
sable tau-rigid modules\, and simplices given by basic tau-rigid modules.
In the case of a cluster-tilted algebra\, it turns out that a tau-tilting
complex corresponds to some positive cluster complex. Due to this fact\, w
e can investigate the structure of a tau-tilting complex of tau-tilting fi
nite type by using the tools of cluster algebra theory. This is joint work
with Haruhisa Enomoto.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arashi Sakai (Nagoya University)
DTSTART:20201112T070000Z
DTEND:20201112T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/2
DESCRIPTION:Title: ICE-closed subcategories and wide tau-tilting modules\nby Arashi Sakai (Nagoya University) as part of Tokyo-Nagoya Algebra Sem
inar\n\n\nAbstract\n多元環の表現論では、多元環上の加群の
なす圏の部分圏が調べられてきた。例えば、torsion class
やwide部分圏などがある。今回の講演ではこれら2つの共
通の一般化であるアーベル圏のICE-closed 部分圏を紹介す
る。そしてICE-closed部分圏はwide 部分圏のtorsion classであ
ることを見る。またsupport tau-tilting 加群の一般化である
wide tau-tilting 加群を導入し、ICE-closed 部分圏がwide tau-tilt
ing 加群と対応することを見る。本公演の内容は榎本悠
久氏との共同研究に基づいている。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Hirano (Kyoto University)
DTSTART:20201203T070000Z
DTEND:20201203T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/3
DESCRIPTION:Title: Full strong exceptional collections for invertible polyn
omials of chain type\nby Yuki Hirano (Kyoto University) as part of Tok
yo-Nagoya Algebra Seminar\n\n\nAbstract\nConstructing a tilting object in
the stable category of graded maximal Cohen-Macaulay modules over a given
graded Gorenstein ring is an important problem in the representation theor
y of graded Gorenstein rings. For a hypersurface S/f in a graded regular r
ing S\, this problem is equivalent to constructing a tilting object in the
homotopy category of graded matrix factorizations of f. In this talk\, we
discuss this problem in the case when S is a polynomial ring\, f is an in
vertible polynomial of chain type and S has a rank one abelian group gradi
ng (called the maximal grading of f)\, and in this case we show the existe
nce of a tilting object arising from a full strong exceptional collection.
This is a joint work with Genki Ouchi.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Matsui (University of Tokyo)
DTSTART:20201210T073000Z
DTEND:20201210T090000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/4
DESCRIPTION:Title: Subcategories of module or derived categories\, and subs
ets of Zariski spectra\nby Hiroki Matsui (University of Tokyo) as part
of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nThe classification problem
of subcategories has been well considered in many areas. This problem was
initiated by Gabriel in 1962 by giving a classification of localizing sub
categories of the module category Mod R via specialization-closed subsets
of the Zariski spectrum Spec R for a commutative noetherian ring. After th
at several authors tried to generalize this result in many ways. For examp
le\, four decades later\, Krause introduced the notion of coherent subsets
of Spec R and used it to classify wide subcategories of Mod R. In this ta
lk\, I will introduce the notions of n-wide subcategories of Mod R and n-c
oherent subsets of Spec R for a (possibly infinite) non-negative integer n
. I will also introduce the notion of n-uniform subcategories of the deriv
ed category D(Mod R) and prove the correspondences among these classes. Th
is result unifies/generalizes many known results such as the classificatio
n given by Gabriel\, Krause\, Neeman\, Takahashi\, Angeleri Hugel-Marks-St
ovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takaha
shi.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (University of Science and Technology of China)
DTSTART:20201217T070000Z
DTEND:20201217T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/6
DESCRIPTION:Title: The finite EI categories of Cartan type\nby Xiao-Wu
Chen (University of Science and Technology of China) as part of Tokyo-Nago
ya Algebra Seminar\n\n\nAbstract\nWe will recall the notion of a finite fr
ee EI category introduced by Li. To each Cartan triple\, we associate a fi
nite free EI category\, called the finite EI category of Cartan type. The
corresponding category algebra is isomorphic to the 1-Gorenstein algebra\,
introduced by Geiss-Leclerc-Schroer\, which is associated to possibly ano
ther Cartan triple. The construction of the second Cartan triple is relate
d to the well-known unfolding of valued graphs. We will apply the obtained
algebra isomorphism to re-interpret some tau-locally free modules as indu
ced modules over a certain skew group algebra. This project is joint with
Ren Wang.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Ohkawa (Kobe University)
DTSTART:20210114T070000Z
DTEND:20210114T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/7
DESCRIPTION:Title: (-2) blow-up formula\nby Ryo Ohkawa (Kobe University
) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nこの講演で
は$A_1$特異点から定まるネクラソフ分配関数について
紹介する. これは特異点解消上の枠付き連接層のモジュ
ライにおける 積分を係数とする母関数である. 特異点
解消として二つ\, 極小解消とスタック的な解消\, つま
り\, 射影平面を位数$2$の巡回群で割った商スタックを
考える. これら二つの特異点解消から定まるネクラソフ
分配関数の 関数等式について紹介する. ひとつは\, 伊
藤-丸吉-奥田が予想した関数等式であり\, もうひとつを
$(-2)$ blow-up formulaとして提案したい. 証明については細
部を省略し\, 望月拓郎氏による壁越え公式について基
本的な例を使って紹介する。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hideya Watanabe (RIMS\, Kyoto University)
DTSTART:20210121T080000Z
DTEND:20210121T093000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/8
DESCRIPTION:Title: Based modules over the $\\imath$-quantum group of type A
I\nby Hideya Watanabe (RIMS\, Kyoto University) as part of Tokyo-Nagoy
a Algebra Seminar\n\n\nAbstract\nIn recent years\, $\\imath$-quantum group
s are intensively studied because of their importance in various branches
of mathematics and physics. Although $\\imath$-quantum groups are thought
of as generalizations of Drinfeld-Jimbo quantum groups\, their representa
tion theory is much more difficult than that of quantum groups. In this t
alk\, I will focus on the $\\imath$-quantum group of type AI. It is a non-
standard quantization of the special orthogonal Lie algebra $\\mathfrak{so
}_n$. I will report my recent research on based modules\, which are modul
es equipped with distinguished bases\, called the $\\imath$-canonical base
s. The first main result is a new combinatorial formula describing the br
anching rule from $\\mathfrak{sl}_n$ to $\\mathfrak{so}_n$. The second on
e is the irreducibility of cell modules associated with the $\\\\imath$-ca
nonical bases.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akishi Ikeda (Josai University)
DTSTART:20210210T070000Z
DTEND:20210210T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/9
DESCRIPTION:Title: Gentle代数の2重次数付きCalabi-Yau完備化と曲
面の幾何学\nby Akishi Ikeda (Josai University) as part of Tokyo-N
agoya Algebra Seminar\n\n\nAbstract\nGentle代数は多元環の表現論
において非常に重要な研究対象であるが\, 近年\, Haiden-K
atzarkov-Kontsevich(HKK)は次数付きgentle代数の導来圏に対し\,
曲面の(位相的)深谷圏との導来同値を与えた. この対応
においては\, 直既約加群と曲面上のあるクラスの弧の
対応が与えられている. 一方\, (punctureの無い)曲面の三
角形分割から現れるquiver with potentialのGinzburg Calabi-Yau(CY)
-3代数の導来圏に対し\, Qiuは(到達可能な)球面対象と曲
面のあるクラスの弧の対応を与えた. このCY-3代数のJacob
i代数はあるクラスのgentle代数になるので\, Qiuによる結
果は\, HKKによる結果の一部をCY-完備化にリフトしたよ
うに見ることもできる.\n\nこの背景に基づき\, この講演
ではまず最初に次数付きgentle代数に付随した2重次数付
きquiver with potential構成法を曲面の深谷圏から来る幾何
学的アイディアに沿って説明し\, そのGinzburg CY代数を用
いて一般的なgentle代数のCY-X完備化の構成について説明
をする. (Xは2重次数の中のコホモロジー的次数とは独立
な方向の次数.) 次に\, このようにして得られたCY-X代数
の導来圏の(到達可能)球面対象が\, ある曲面の無限巡回
被覆として得られる被覆空間の中の弧と対応するとい
う\, QiuのCY-3の場合の結果の一般化\, あるいはHKKの結果
のCY完備化へのリフトに相当する結果について説明をす
る. 時間があれば\, Xを整数Nに特殊化することで曲面のN
角形分割に付随したquiver with potentialの構成になってい
ることについても説明をしたいと考えている. この結果
は\, Yu Qiu氏\, Yu Zhou氏との共同研究に基づく.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunya Saito (Nagoya University)
DTSTART:20210224T070000Z
DTEND:20210224T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/10
DESCRIPTION:Title: 周期三角圏上の傾理論\nby Shunya Saito (Na
goya University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\n
周期三角圏とは、シフト関手のある累乗が恒等関手に
なる三角圏であり、Cohen-Macaulay表現論や自己移入多元環
の表現論で自然に姿を現す。このような三角圏は周期
性から傾対象を決して持たず、特に代数上の導来圏と
三角同値にならないことが知られている。本講演では
、傾理論の周期三角圏における類似である周期傾理論
について紹介する。まず、導来圏の周期類似である周
期導来圏について説明し、周期傾対象を持つ三角圏は
周期導来圏と三角同値になるという周期傾定理を紹介
する。最後に、DG代数を用いた証明手法について触れる
。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akihito Wachi (Hokkaido University of Education)
DTSTART:20210311T070000Z
DTEND:20210311T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/11
DESCRIPTION:Title: 相対不変式で生成されるゴレンスタイン
環のレフシェッツ性\nby Akihito Wachi (Hokkaido University of
Education) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\n可換
環論にアルチン次数環のレフシェッツ性の問題がある
。これは、コホモロ ジー環が満たす性質を抽出した性
質である。表現論的に興味のある環、例えば、 複素鏡
映群の余不変式環のほぼすべてがレフシェッツ性を持
つことが証明され ていたり、Schur-Weyl双対性に関わる環
がレフシェッツ性を持つことも知られ ている。\n\n他方
、斉次多項式 F が与えられたとき、別の多項式を微分
作用素と見て F に 作用させることを考え、Fを消す多項
式全体のなすイデアルによる剰余環を作る と、アルチ
ンゴレンスタイン次数環が得られる。そこで、多項式 F
が与えられ たとき、こうして作られる環がレフシェッ
ツ性を持つかどうかという問題が考 えられる。\n\n例え
ば、F が単項式や差積などの場合はレフシェッツ性が証
明されているが、 レフシェッツ性を持つための F の条
件は一般には何も知られていない。この講 演では、F
が行列式、対称行列の行列式、パフィアン等の場合に
レフシェッツ 性が証明されることを紹介する。\n\nこれ
らのレフシェッツ性は概均質ベクトル空間の正則性と
の関係があり、また、 証明に一般Verma加群を用いるな
ど、可換環論の問題ではあるが表現論が活用 できるこ
とを中心に話したい。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (University of Sydney)
DTSTART:20210408T070000Z
DTEND:20210408T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/12
DESCRIPTION:Title: Abelian envelopes of monoidal categories\nby Kevin
Coulembier (University of Sydney) as part of Tokyo-Nagoya Algebra Seminar\
n\n\nAbstract\nFor the purposes of this talk\, a ‘tensor category’ is
an abelian rigid monoidal category\, linear over some field. I will try to
argue that there are good reasons (inspired by classification attempts of
tensor categories\, by motives\, by Frobenius twists on tensor categories
and by the idea of universal tensor categories)\, to try to associate ten
sor categories to non-abelian rigid monoidal categories. Then I will comme
nt on some of the recent progress made on such constructions (in work of B
enson\, Comes\, Entova\, Etingof\, Heidersdof\, Hinich\, Ostrik\, Serganov
a and myself).\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Külshammer (Uppsala University)
DTSTART:20210422T070000Z
DTEND:20210422T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/13
DESCRIPTION:Title: Exact categories via $A_\\infty$-algebras\nby Julia
n Külshammer (Uppsala University) as part of Tokyo-Nagoya Algebra Semi
nar\n\n\nAbstract\nMany instances of extension closed subcategories appear
throughout representation theory\, e.g. filtered modules\, Gorenstein pro
jectives\, as well as modules of finite projective dimension. In the first
part of the talk\, I will outline a general strategy to realise such subc
ategories as categories of induced modules from a subalgebra using $A_\\in
fty$-algebras. In the second part\, I will describe how this strategy has
been successfully applied for the exact category of filtered modules over
a quasihereditary algebra. In particular I will present compatibility resu
lts of this approach with heredity ideals in a quasihereditary algebra fro
m joint work with Teresa Conde.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Charles University)
DTSTART:20210506T070000Z
DTEND:20210506T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/14
DESCRIPTION:Title: Derived quotients of Cohen-Macaulay rings\nby Liran
Shaul (Charles University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nA
bstract\nIt is well known that if A is a Cohen-Macaulay ring and $a_1\,\\d
ots\,a_n$ is an $A$-regular sequence\, then the quotient ring $A/(a_1\,\\d
ots\,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by
deriving the quotient operation\, if A is a Cohen-Macaulay ring and $a_1\,
\\dots\,a_n$ is any sequence of elements in $A$\, the derived quotient of
$A$ with respect to $(a_1\,\\dots\,a_n)$ is Cohen-Macaulay. Several applic
ations of this result are given\, including a generalization of Hironaka's
miracle flatness theorem to derived algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Kanda (Osaka City University)
DTSTART:20210520T070000Z
DTEND:20210520T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/15
DESCRIPTION:Title: Flat cotorsion modules over Noether algebras\nby Ry
o Kanda (Osaka City University) as part of Tokyo-Nagoya Algebra Seminar\n\
n\nAbstract\nThis talk is based on joint work with Tsutomu Nakamura. For a
module-finite algebra over a commutative noetherian ring\, we give a comp
lete description of flat cotorsion modules in terms of prime ideals of the
algebra\, as a generalization of Enochs' result for a commutative noether
ian ring. As a consequence\, we show that pointwise Matlis duality gives a
bijective correspondence between the isoclasses of indecomposable flat co
torsion right modules and the isoclasses of indecomposable injective left
modules. This correspondence is an explicit realization of Herzog's homeom
orphism induced from elementary duality between Ziegler spectra.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Murai (Waseda University)
DTSTART:20210602T070000Z
DTEND:20210602T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/16
DESCRIPTION:Title: An equivariant Hochster's formula for $S_n$-invariant m
onomial ideals\nby Satoshi Murai (Waseda University) as part of Tokyo-
Nagoya Algebra Seminar\n\n\nAbstract\n組合せ可換環論の分野では
、多項式環の単項式イデアルや二項式イデアルの代\n数
的な情報と凸多面体や単体的複体の組合せ論的な情報
の関連がよく研究され\nる。イデアルの自由分解に関す
るHochsterの公式は、(squarefreeな)単項式イデ\nアルの自由
分解のベッチ数と単体的複体のホモロジーとの関係を
与える公式で、\n組合せ可換代数の分野における基本的
な結果の一つである。本講演では、$n$変\n数多項式環$S=
K[x_1\,\\dots\,x_n]$の単項式イデアル$I$が$n$次対称群の作用
で固\n定されるときは、ベッチ数$\\beta_{ij}(I)=\\dim_K \\math
rm{Tor}_i(I\,K)_j$のみ\nならず、$\\mathrm{Tor}_i(I\,K)_j$の表現
の情報まで単体的複体のホモロジーを\n用いて計算でき
ることを紹介する。\n\n 対称群の作用で固定される単
項式イデアルの性質を調べた今回の研究結果は、\n無限
変数多項式環上のイデアルで無限対称群の作用で固定
されるイデアルにある\n種の有限生成性があること(Noeth
erianity up to symmetry)に関連する研究を動\n機としている。
講演の前半ではこの問題の背景について簡単に話をし
、後半に今\n回の結果とその応用について紹介したい。
\n\n 本研究はClaudiu Raicuとの共同研究である。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kohei Kikuta (Chuo University)
DTSTART:20210624T070000Z
DTEND:20210624T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/17
DESCRIPTION:Title: Rank 2 free subgroups in autoequivalence groups of Cala
bi-Yau categories\nby Kohei Kikuta (Chuo University) as part of Tokyo-
Nagoya Algebra Seminar\n\n\nAbstract\nVia homological mirror symmetry\, th
ere is a relation between autoequivalence groups of derived categories of
coherent sheaves on Calabi-Yau varieties\, and the symplectic mapping clas
s groups of symplectic manifolds. In this talk\, as an analogue of mapping
class groups of closed oriented surfaces\, we study autoequivalence group
s of Calabi-Yau triangulated categories. In particular\, we consider embed
dings of rank 2 (non- commutative) free groups generated by spherical twis
ts. It is interesting that the proof of main results is almost similar to
that of corresponding results in the theory of mapping class groups.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsukasa Ishibashi (RIMS\, Kyoto University)
DTSTART:20210708T070000Z
DTEND:20210708T083000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/18
DESCRIPTION:Title: Sign-stable mutation loops and pseudo-Anosov mapping cl
asses\nby Tsukasa Ishibashi (RIMS\, Kyoto University) as part of Tokyo
-Nagoya Algebra Seminar\n\n\nAbstract\n箙の変異ループは対応す
るクラスター代数およびクラスター多様体上の自己同
型を誘導し、特にこれを繰り返し作用させることで離
散力学系が定まる. 石橋-狩野 (Geom. Dedicata\, 2021) では曲
面上の写像類の擬Anosov性の類似として変異ループの符
号安定性と呼ばれる一連の性質を導入し\, 符号安定性
のもとでクラスター多様体への作用の代数的エントロ
ピーの計算などの応用を得た. 本講演では点付き曲面上
の写像類から定まる変異ループについて\, 擬Anosov性と
種々の符号安定性との比較を行う. 本講演の内容は東北
大学の狩野隼輔氏との共同研究に基づく.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kozakai (Tokyo Science University)
DTSTART:20211119T080000Z
DTEND:20211119T093000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/19
DESCRIPTION:Title: 有限群のブロック上の$\\tau$-傾理論\nby
Yuta Kozakai (Tokyo Science University) as part of Tokyo-Nagoya Algebra S
eminar\n\n\nAbstract\nAdachi-Iyama-Reiten(2014)により導入された台
$\\tau$-傾加群は\, 2項準傾複体や半煉瓦\, 2項単純系とい
った\,\nさまざまな表現論的に重要な対象と1対1で対応
する。そのため\, 近年では\, 与えられた有限次元多元
環に対して\,\nそれらの上での台$\\tau$-傾加群や\, それ
らに対応する対象たちの研究が盛んに行われている。
本講演では\,\n$k$を標数$p>0$の代数的閉体とし\, 有限群$\
\tilde{G}$と\, $\\tilde{G}$の正規部分群$G$\,\n群環$kG$のブロ
ック$B$\, $B$を被覆する$k\\tilde{G}$のブロック$\\tilde{B}$に
対して\,\nより複雑な構造をもつ$\\tilde{B}$上の台$\\tau$-
傾加群や2項準傾複体\, 半煉瓦\, 2項単純系が\, $B$上のそ
れらから\,\n有限群の表現論的な道具を用いて得られる
ことを説明する。さらに\, 剰余群$\\tilde{G}/G$が$p$-群の
ときには\,\n$B$上の台$\\tau$-傾加群全体の集合は\, $\\tilde
{B}$上のそれと\, 半順序集合として同型となることも説
明する。\n本講演は、東京理科大学の小塩遼太郎氏との
共同研究に基づく。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Cologne)
DTSTART:20211216T074500Z
DTEND:20211216T091500Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/20
DESCRIPTION:Title: Cyclic polytopes and higher Auslander-Reiten theory
\nby Nicholas Williams (University of Cologne) as part of Tokyo-Nagoya Alg
ebra Seminar\n\n\nAbstract\nOppermann and Thomas show that tilting modules
over Iyama’s higher\nAuslander algebras of type A are in bijection with
triangulations of\neven-dimensional cyclic polytopes. Triangulations of c
yclic polytopes\nare partially ordered in two natural ways known as the hi
gher\nStasheff-Tamari orders\, which were introduced in the 1990s by\nKapr
anov\, Voevodsky\, Edelman\, and Reiner as higher-dimensional\ngeneralisat
ions of the Tamari lattice. These two partial orders were\nconjectured to
be equal in 1996 by Edelman and Reiner\, and we prove\nthat this conjectur
e is true. \n\nWe further show how the higher\nStasheff-Tamari orders corr
espond in even dimensions to natural orders\non tilting modules which were
studied by Riedtmann\, Schofield\, Happel\,\nand Unger. This then allows
us to complete the picture of Oppermann\nand Thomas by showing that triang
ulations of odd-dimensional cyclic\npolytopes correspond to equivalence cl
asses of d-maximal green\nsequences\, which we introduce as higher-dimensi
onal analogues of\nKeller’s maximal green sequences. We show that the hi
gher\nStasheff-Tamari orders correspond to natural orders on equivalence\n
classes of d-maximal green sequences\, which relate to the no-gap\nconject
ure of Brustle\, Dupont\, and Perotin. The equality of the higher\nStashef
f-Tamari orders then implies that these algebraic orders on\ntilting modul
es and d-maximal green sequences are equal. If time\npermits\, we will als
o discuss some results on mutation of\ncluster-tilting objects and triangu
lations.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Prefecture University)
DTSTART:20220118T060000Z
DTEND:20220118T073000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/21
DESCRIPTION:Title: Exact-categorical properties of subcategories of abelia
n categories\nby Haruhisa Enomoto (Osaka Prefecture University) as par
t of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nQuillen's exact category
is a powerful framework for studying extension-closed subcategories of abe
lian categories\, and provides many interesting questions on such subcateg
ories. In the first talk\, I will explain the basics of some properties an
d invariants of exact categories (e.g. the Jordan-Holder property\, simple
objects\, and Grothendieck monoid). In the second talk\, I will give some
results and questions about particular classes of exact categories arisin
g in the representation theory of algebras (e.g. torsion(-free) classes ov
er path algebras and preprojective algebras). If time permits\, I will dis
cuss questions of whether these results can be generalized to extriangulat
ed categories (extension-closed subcategories of triangulated categories).
\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Prefecture University)
DTSTART:20220121T074500Z
DTEND:20220121T091500Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/22
DESCRIPTION:Title: Exact-categorical properties of subcategories of abelia
n categories 2\nby Haruhisa Enomoto (Osaka Prefecture University) as p
art of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nQuillen's exact categor
y is a powerful framework for studying extension-closed subcategories of a
belian categories\, and provides many interesting questions on such subcat
egories. In the first talk\, I will explain the basics of some properties
and invariants of exact categories (e.g. the Jordan-Holder property\, simp
le objects\, and Grothendieck monoid). In the second talk\, I will give so
me results and questions about particular classes of exact categories aris
ing in the representation theory of algebras (e.g. torsion(-free) classes
over path algebras and preprojective algebras). If time permits\, I will d
iscuss questions of whether these results can be generalized to extriangul
ated categories (extension-closed subcategories of triangulated categories
).\n\nThis talk is the second half of the lecture series.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigeo Koshitani (Chiba University)
DTSTART:20220309T040000Z
DTEND:20220309T053000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/23
DESCRIPTION:Title: Modular representation theory of finite groups – loca
l versus global\nby Shigeo Koshitani (Chiba University) as part of Tok
yo-Nagoya Algebra Seminar\n\n\nAbstract\nWe are going to talk about repres
entation theory of finite groups. In the 1st part it will be on "Equivalen
ces of categories ” showing up for block theory in modular representatio
n theory\, and it should be kind of introductory lecture/talk. So the audi
ence is supposed to have knowledge only of definitions of groups\, rings\,
fields\, modules\, and so on. In the 2nd part we will discuss kind of loc
al—global conjectures in modular representation theory of finite groups\
, that originally and essentially are due to Richard Brauer (1901–77).\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigeo Koshitani (Chiba University)
DTSTART:20220311T040000Z
DTEND:20220311T053000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/24
DESCRIPTION:Title: Modular representation theory of finite groups – loca
l versus global (part 2)\nby Shigeo Koshitani (Chiba University) as pa
rt of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nWe are going to talk abo
ut representation theory of finite groups. In the 1st part it will be on "
Equivalences of categories ” showing up for block theory in modular repr
esentation theory\, and it should be kind of introductory lecture/talk. So
the audience is supposed to have knowledge only of definitions of groups\
, rings\, fields\, modules\, and so on. In the 2nd part we will discuss ki
nd of local—global conjectures in modular representation theory of finit
e groups\, that originally and essentially are due to Richard Brauer (1901
–77).\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Osaka Metropolitan University)
DTSTART:20220413T013000Z
DTEND:20220413T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/25
DESCRIPTION:Title: Tilting ideals of deformed preprojective algebras\n
by Yuta Kimura (Osaka Metropolitan University) as part of Tokyo-Nagoya Alg
ebra Seminar\n\n\nAbstract\nLet $K$ be a field and $Q$ a finite quiver.\nF
or a weight $\\lambda \\in K^{|Q_0|}$\, the deformed preprojective\nalgebr
a $\\Pi^{\\lambda}$ was introduced by Crawley-Boevey and Holland\nto study
deformations of Kleinian singularities.\nIf $\\lambda = 0$\, then $\\Pi^{
0}$ is the preprojective algebra\nintroduced by Gelfand-Ponomarev\, and ap
pears many areas of\nmathematics.\nAmong interesting properties of $\\Pi^{
0}$\, the classification of\ntilting ideals of $\\Pi^{0}$\, shown by Buan-
Iyama-Reiten-Scott\, is\nfundamental and important.\nThey constructed a bi
jection between the set of tilting ideals of\n$\\Pi^{0}$ and the Coxeter g
roup $W_Q$ of $Q$.\n\nIn this talk\, when $Q$ is non-Dynkin\, we see that
$\\Pi^{\\lambda}$ is a\n$2$-Calabi-Yau algebra\, and show that there exist
s a bijection between\ntilting ideals and a Coxeter group.\nHowever $W_Q$
does not appear\, since $\\Pi^{\\lambda}$ is not necessary basic.\nInstead
of $W_Q$\, we consider the Ext-quiver of rigid simple modules\,\nand use
its Coxeter group.\nWhen $Q$ is an extended Dynkin quiver\, we see that th
e Ext-quiver is\nfinite and this has an information of singularities of a\
nrepresentation space of semisimple modules.\nThis is joint work with Will
iam Crawley-Boevey.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiko Yoshinaga (Osaka University)
DTSTART:20220601T013000Z
DTEND:20220601T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/26
DESCRIPTION:Title: 超平面配置の特性準多項式\nby Masahiko Y
oshinaga (Osaka University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nA
bstract\n$n$ ベクトル空間内の $(n-1)$ 次元（アフィン）部
分空間のいくつかの集まりを超平面配置という。ルー
ト系、コクセター群、配置空間など様々な文脈で自然
に表れる対象である。超平面配置の重要な不変量の一
つとして「特性多項式」が挙げられる。特性多項式は
（実配置の）部屋数、（複素配置の）補集合のポアン
カレ多項式、（有限体上の）点の数など様々な情報を
持っている。本講演では、アフィンルート系のある種
の有限部分配置を主な対象に、特性多項式の性質や計
算方法を、特に 2007年に Kamiya-Takemura-Terao により導入さ
れた「特性準多項式」に焦点をあてて紹介する。特性
準多項式は特性多項式の精密化であるだけでなく、当
初から多面体のEhrhart理論（格子点の数え上げ理論）と
の密接な関係が示唆されていた。特性多項式よりは複
雑で扱いにくい側面もあるが、その複雑さの中に、代
数的トーラス内のトーラス配置の位相幾何的情報や多
面体の対称性に関する情報が見えてくるという最近の
研究を紹介したい。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiko Yoshinaga (Osaka University)
DTSTART:20220608T013000Z
DTEND:20220608T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/27
DESCRIPTION:Title: 超平面配置の特性準多項式\nby Masahiko Y
oshinaga (Osaka University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nA
bstract\n$n$ ベクトル空間内の $(n-1)$ 次元（アフィン）部
分空間のいくつかの集まりを超平面配置という。ルー
ト系、コクセター群、配置空間など様々な文脈で自然
に表れる対象である。超平面配置の重要な不変量の一
つとして「特性多項式」が挙げられる。特性多項式は
（実配置の）部屋数、（複素配置の）補集合のポアン
カレ多項式、（有限体上の）点の数など様々な情報を
持っている。本講演では、アフィンルート系のある種
の有限部分配置を主な対象に、特性多項式の性質や計
算方法を、特に 2007年に Kamiya-Takemura-Terao により導入さ
れた「特性準多項式」に焦点をあてて紹介する。特性
準多項式は特性多項式の精密化であるだけでなく、当
初から多面体のEhrhart理論（格子点の数え上げ理論）と
の密接な関係が示唆されていた。特性多項式よりは複
雑で扱いにくい側面もあるが、その複雑さの中に、代
数的トーラス内のトーラス配置の位相幾何的情報や多
面体の対称性に関する情報が見えてくるという最近の
研究を紹介したい。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (Freiburg University)
DTSTART:20220622T080000Z
DTEND:20220622T093000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/28
DESCRIPTION:Title: Update on singular equivalences between commutative rin
gs\nby Martin Kalck (Freiburg University) as part of Tokyo-Nagoya Alge
bra Seminar\n\n\nAbstract\nWe will start with an introduction to singulari
ty categories\, which\n were first studied by Buchweitz and later r
ediscovered by Orlov.\n Then we will explain what is known about tr
iangle equivalences between\n singularity categories of commutative
rings\, recalling results of\n Knörrer\, D. Yang (based on our jo
int works on relative singularity\n categories. This result also fo
llows from work of Kawamata and was\n generalized in a joint work w
ith Karmazyn) and a new equivalence\n obtained in arXiv:2103.06584.
\n\n In the remainder of the talk\, we will focus on the case of Go
renstein\n isolated singularities and especially hypersurfaces\, wh
ere we give a\n complete description of quasi-equivalence classes o
f dg enhancements\n of singularity categories\, answering a questio
n of Keller & Shinder.\n This is based on arXiv:2108.03292.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220615T013000Z
DTEND:20220615T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/29
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 1<
/a>\nby Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Al
gebra Seminar\n\n\nAbstract\nIn this series of three talks\, we expand upo
n the previous talk (see attached link to the slides) given\nat the semina
r and study the relationship between cyclic polytopes and\nhigher Auslande
r--Reiten theory in more detail.\n\nIn the first talk\, we focus on cyclic
polytopes. We survey important\nproperties of cyclic polytopes\, such as
different ways to construct\nthem\, the Upper Bound Theorem\, and their Ra
msey-theoretic properties.\nWe then move on to triangulations of cyclic po
lytopes. We give\nefficient combinatorial descriptions of triangulations o
f\neven-dimensional and odd-dimensional cyclic polytopes\, which we will\n
use in subsequent talks. We finally define the higher Stasheff--Tamari\nor
ders on triangulations of cyclic polytopes. We give important\nresults on
the orders\, including Rambau's Theorem\, and the equality of\nthe two ord
ers.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220629T013000Z
DTEND:20220629T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/30
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 2<
/a>\nby Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Al
gebra Seminar\n\n\nAbstract\nIn the second talk\, we focus on higher Ausla
nder--Reiten theory. We survey the basic setting of this theory\, starting
with d-cluster-tilting subcategories of module categories. We then move o
n to d-cluster-tilting subcategories of derived categories in the case of
d-representation-finite d-hereditary algebras. We explain how one can cons
truct (d + 2)-angulated cluster categories for such algebras\, generalisin
g classical cluster categories. We finally consider the d-almost positive
category\, which is the higher generalisation of the category of two-term
complexes. Throughout\, we illustrate the results using the higher Ausland
er algebras of type A\, and explain how the different categories can be in
terpreted combinatorially for these algebras.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220706T013000Z
DTEND:20220706T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/31
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 3<
/a>\nby Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Al
gebra Seminar\n\n\nAbstract\nIn the third talk\, we consider the relations
hip between the objects from the first two talks. We explain how triangula
tions of even-dimensional cyclic polytopes may be interpreted in terms of
tilting modules\, cluster-tilting objects\, or d-silting complexes. We the
n proceed in the d-silting framework\, and show how the higher Stasheff--T
amari orders may be interpreted algebraically for even dimensions. We expl
ain how this allows one to interpret odd-dimensional triangulations algebr
aically\, namely\, as equivalence classes of d-maximal green sequences. We
briefly digress to consider the issue of equivalence of maximal green seq
uences itself. We then show how one can interpret the higher Stasheff--Tam
ari orders on equivalence classes of d-maximal green sequences. We finish
by drawing out some consequences of this algebraic interpretation of the h
igher Stasheff--Tamari orders.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Imamura (Osaka University)
DTSTART:20220720T013000Z
DTEND:20220720T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/32
DESCRIPTION:Title: Grothendieck enriched categories\nby Yuki Imamura (
Osaka University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nG
rothendieck圏は、入射的余生成子の存在や随伴関手定理の
成立など、アーベル圏の中でも特に良い性質を持つこ
とで知られる。通常Grothendieck圏は、生成子を持つ余完
備なアーベル圏であって、フィルター余極限を取る関
手が完全関手になるような圏として内在的な性質で以
て定義されるが、加群圏の"良い部分圏"として実現でき
るという外在的な特徴づけ(Gabriel-Popescuの定理)も存在す
る。アーベル圏が自然なプレ加法圏(アーベル群の圏Ab
上の豊穣圏)の構造を持つことから、Gabriel-Popescuの定理
はAb-豊穣圏に対する定理だと思うことができる。本講
演では、より一般のGrothendieckモノイダル圏V上の豊穣圏
に対してGabriel-Popescuの定理の一般化を定式化し証明す
る。特にVとしてアーベル群の複体の圏Chを取ることに
よりGrothendieck圏のdg圏類似とそのGabriel-Popescuの定理が得
られることも確認する。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (Freiburg University)
DTSTART:20221020T074000Z
DTEND:20221020T091000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/33
DESCRIPTION:Title: A surface and a threefold with equivalent singularity c
ategories\nby Martin Kalck (Freiburg University) as part of Tokyo-Nago
ya Algebra Seminar\n\n\nAbstract\nWe discuss a triangle equivalence betwee
n singularity categories of an affine surface and an affine threefold. Bot
h are isolated cyclic quotient singularities. This seems to be the first (
non-trivial) example of a singular equivalence involving varieties of even
and odd Krull dimension.\n\nThe same approach recovers a result of Dong Y
ang showing a singular equivalence between certain cyclic quotient singula
rities in dimension 2 and certain finite dimensional commutative algebras.
\n\nThis talk is based on https://arxiv.org/pdf/2103.06584.pdf\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunske Kano (Tohoku University)
DTSTART:20230120T013000Z
DTEND:20230120T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/34
DESCRIPTION:Title: Tropical cluster transformations and train track splitt
ings\nby Shunske Kano (Tohoku University) as part of Tokyo-Nagoya Alge
bra Seminar\n\n\nAbstract\nFock-Goncharovは箙に対し、クラスター
代数と呼ばれる組み合わせ構造を持つような概形であ
るクラスター多様体を定義した。 この概形は良い正値
性を持つことから、半体値集合を考えることができる
。 箙が点付き曲面の三角形分割から得られるとき、ト
ロピカル半体値集合は曲面の測度付き葉層構造の空間
の適切な拡張と同一視される。 クラスター多様体のト
ロピカル半体値集合はクラスター構造から定まるPL構造
を持つが、一方で曲面の測度付き葉層構造の空間には
トレイントラックと呼ばれるグラフを用いたPL構造が定
まることが知られている。 本講演では、Goncharov-Shenの
クラスター多様体上のLandau-Ginzburgポテンシャル関数の
トロピカル化を通してトレイントラックを翻訳し、2つ
のPL構造が同値であることを確認する。 またこのトレ
イントラックの翻訳を通して、一般の擬Anosov写像類が
符号安定性と呼ばれる性質を持つことを説明する。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (University of Glasgow)
DTSTART:20230220T080000Z
DTEND:20230220T093000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/35
DESCRIPTION:Title: Silting discrete代数上のsemibrick複体とspherical
objects\nby Wahei Hara (University of Glasgow) as part of Tokyo-Nagoy
a Algebra Seminar\n\n\nAbstract\nSilting discrete代数は導来圏のt構
造に関してある種の離散性を満たす有限次元代数であ
り，代数の表現論の分野で研究されている．(semi)brick複
体は導来圏の対象であって，単純加群(の直和)が持つ性
質を一般化した条件で定義される．本講演ではまず「si
lting discrete代数上のsemibrick複体は，実際にとある有界t
構造の核として現れる部分Abel圏の単純対象の直和であ
る」という分類結果について紹介する．実際はより強
く，負の次数の自己Extが消滅するという条件で，ある
有界t構造の核に含まれる対象が特徴づけられるという
定理を証明し，semibrick複体の分類はその系となる．\n\n
後半では幾何学的な側面について紹介する．ある3次元
フロップ収縮に対して，Donovan-Wemyssによって定義された
contraction algebraという有限次元代数はsilting discrete代数の
例を与える．このときbrick複体はSeidel-Thomasによって定
義されたspherical objectの一般化として捉えることができ
，代数幾何やシンプレクティック幾何において自己同
値群の決定問題やBridgeland安定性条件の空間の連結性の
問題と絡む，幾何学的にも重要な対象である．この背
景をもう少し詳しく整理したのち，前半のsemibrick複体
の分類結果で用いる手法がこの幾何学的状況にも拡張
し，この分野の中心問題のひとつであるspherical objectの
分類定理を導くことを紹介する．同様の手法は2次元Klei
nian特異点の部分クレパント解消に対しても機能し，こ
れら全ての状況で，null圏と呼ばれる導来圏の部分三角
圏の有界t構造の分類や，Bridgeland安定性条件の空間の連
結性などを導く．本講演の内容は全てMichael Wemyss氏との
共同研究です．\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kota Murakami (Tokyo University)
DTSTART:20230421T040000Z
DTEND:20230421T053000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/36
DESCRIPTION:Title: Categorifications of deformed Cartan matrices\nby K
ota Murakami (Tokyo University) as part of Tokyo-Nagoya Algebra Seminar\n\
n\nAbstract\nIn a series of works of Geis-Leclerc-Schroer\, they introduce
d a version of preprojective algebra associated with a symmetrizable gener
alized Cartan matrix and its symmetrizer. For finite type\, it can be rega
rded as an un-graded analogue of Jacobian algebra of certain quiver with p
otential appeared in the theory of (monoidal) categorification of cluster
algebras.\n\nIn this talk\, we will present an interpretation of graded st
ructures of the preprojective algebra of general type\, in terms of a mult
i-parameter deformation of generalized Cartan matrix and relevant combinat
orics motivated from several contexts in the theory of quantum loop algebr
as or quiver $\\mathcal{W}$-algebras. From the vantage point of the repres
entation theory of preprojective algebra\, we will prove several purely co
mbinatorial properties of these concepts. This talk is based on a joint wo
rk with Ryo Fujita (RIMS).\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takumi Otani (Osaka University)
DTSTART:20230428T040000Z
DTEND:20230428T053000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/37
DESCRIPTION:Title: Full exceptional collections associated with Bridgeland
stability conditions\nby Takumi Otani (Osaka University) as part of T
okyo-Nagoya Algebra Seminar\n\n\nAbstract\nThe space of Bridgeland stabili
ty conditions on a triangulated category is important in mirror symmetry a
nd many people develop various techniques to study it. In order to study t
he homotopy type of the space of stability conditions\, Macri studied stab
ility conditions associated with full exceptional collections. Based on hi
s work\, Dimitrov-Katzarkov introduced the notion of a full σσ-exception
al collection for a stability condition σσ.\n\nIn this talk\, I will exp
lain the relationship between full exceptional collections and stability c
onditions and some properties. I will also talk about the existence of ful
l σσ-exceptional collections for the derived category of an acyclic quiv
er.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine de Saint Germain (University of Hong Kong)
DTSTART:20230516T060000Z
DTEND:20230516T073000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/38
DESCRIPTION:Title: Cluster-additive functions and frieze patterns with coe
fficients\nby Antoine de Saint Germain (University of Hong Kong) as pa
rt of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nIn his study of combinat
orial features of cluster categories and cluster-tilted algebras\, Ringel
introduced an analogue of additive functions of stable translation quivers
called cluster-additive functions.\n\nIn the first part of this talk\, we
will define cluster-additive functions associated to any acyclic mutation
matrix\, relate them to mutations of the cluster X variety\, and realise
their values as certain compatibility degrees between functions on the clu
ster A variety associated to the Langlands dual mutation matrix (in accord
ance with the philosophy of Fock-Goncharov). This is based on joint work w
ith Peigen Cao and Jiang-Hua Lu. In the second part of this talk\, we will
introduce the notion of frieze patterns with coefficients based on joint
work with Min Huang and Jiang-Hua Lu. We will then discuss their connectio
n with cluster-additive functions.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hideto Asashiba
DTSTART:20230707T060000Z
DTEND:20230707T073000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/39
DESCRIPTION:Title: クイバー表現のパーシステンス加群への
応用: 区間加群による近似と分解\nby Hideto Asashiba as pa
rt of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\n位相的データ解析
では，入力データーは，d次元ユークリッド空間内の有
限個の点からなる集合"点雲" P の形で与えられ，各 r = 0
\, 1\, ...\, d に対して，パーシステントホモロジー群H_r(P
)が計算される。これはある自然数nに対する，同方向A_n
型クイバーQのある体k上の表現になっている。Gabrielの
定理より，直既約表現の完全代表系は"区間"表現 V_I (I:=
[a\,b]\, 1 ≦ a ≦ b ≦ n)の全体で与えられる。Qの各表現M
に対して，d_M(I)をMの直既約分解におけるV_Iの重複度と
すると，列d_M:= (d_M(I))_I は同型のもとでのMの完全不変
量になっている。この重複度をkQのAuslander-Reiten quiver上
にプロットした図をMのパーシステント図とよぶ。族(H_r
(P))_r はPに関する重要な情報を保存し，応用研究で活用
されるが，パーシステント図d_{H_r(P)}を用いて，これを
解析することができる。次にPが他のパラメーター，例
えば時間とともに変化する場合，この方法により2次元
パーシステンス加群が定義され，さらに多次元に一般
化される。これが位相的データ解析での代数的アプロ
ーチの主な研究対象になる。一般にm次元パーシステン
ス加群はm次元格子の形のクイバーQに関係式を入れた多
元環上の加群と理解される。この場合1次元の場合と異
なり多元環はほとんどワイルド表現型になるため，リ
アルタイムで直既約加群の重複度d_Mを計算しそれを比
較するのは困難になる。上に述べたもとの意味の区間
表現は，Q上の連結かつ凸な部分クイバーを台とする"区
間加群"に一般化される。d_Mの代わりにMのこれら区間加
群の直和によってMを近似することによりリアルタイム
性を保証する方法が考えられる。この講演では2通りの
意味の近似を提示しそれらの関係を与える。\nこの講演
は，エスカラ，中島，吉脇の各氏との共同研究に基づ
く。\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART:20230714T013000Z
DTEND:20230714T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/40
DESCRIPTION:Title: Local Forms of Noncommutative Functions and Application
s\nby Michael Wemyss (University of Glasgow) as part of Tokyo-Nagoya A
lgebra Seminar\n\n\nAbstract\nThis talk will explain how Arnold's results
for commutative\nsingularities can be extended into the noncommutative set
ting\, with\nthe main result being a classification of certain Jacobi alge
bras\narising from (complete) free algebras. This class includes finite\nd
imensional Jacobi algebras\, and also Jacobi algebras of GK dimension\none
\, suitably interpreted. The surprising thing is that a\nclassification sh
ould exist at all\, and it is even more surprising\nthat ADE enters.\n\nI
will spend most of my time explaining what the algebras are\, what\nthey c
lassify\, and how to intrinsically extract ADE information from\nthem. At
the end\, I'll explain why I'm really interested in this\nproblem\, an upd
ate including results on different quivers\, and the\napplications of the
above classification to curve counting and\nbirational geometry. This is j
oint work with Gavin Brown.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Ren (Kansai University)
DTSTART:20231012T013000Z
DTEND:20231012T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/41
DESCRIPTION:Title: $q$-deformed rational numbers\, Farey sum and a 2-Calab
i-Yau category of $A_2$ quiver\nby Xin Ren (Kansai University) as p
art of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nLet $q$ be a positive r
eal number. The left and right $q$-deformed rational numbers were introduc
ed by Bapat\, Becker and Licata via regular continued fractions\, and the
right $q$-deformed rational number is exactly $q$-deformed rational number
considered by Morier-Genoud and Ovsienko\, when $q$ is a formal parameter
. They gave a homological interpretation for left and right $q$-deformed r
ational numbers by considering a special 2-Calabi–Yau category associate
d to the $A_2$ quiver.\n\nIn this talk\, we begin by introducing the above
definitions and related results. Then we give a formula for computing the
$q$-deformed Farey sum of the left $q$-deformed rational numbers based on
the negative continued fractions. We combine the homological interpretati
on of the left and right $q$-deformed rational numbers and the $q$-deforme
d Farey sum\, and give a homological interpretation of the $q$-deformed Fa
rey sum. We also apply the above results to real quadratic irrational numb
ers with periodic type.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (University of Science and Technology of China)
DTSTART:20231214T013000Z
DTEND:20231214T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/42
DESCRIPTION:Title: On exact dg categories\nby Xiaofa Chen (University
of Science and Technology of China) as part of Tokyo-Nagoya Algebra Semina
r\n\n\nAbstract\nIn this talk\, I will give an introduction to exact dg ca
tegories and then explore their application to various correspondences in
representation theory. We will generalize the Auslander–Iyama correspond
ence\, the Iyama–Solberg correspondence\, and a correspondence considere
d in a paper by Iyama in 2005 to the setting of exact dg categories. The s
logan is that solving correspondence-type problems becomes easier using dg
categories\, and interesting phenomena emerge when the dg category is con
centrated in degree zero or is abelian.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (Okinawa Institute of Science and Technology)
DTSTART:20231225T013000Z
DTEND:20231225T030000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/43
DESCRIPTION:Title: Rigidity of bricks and brick-Brauer-Thrall conjectures
I\nby Kaveh Mousavand (Okinawa Institute of Science and Technology) as
part of Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (Okinawa Institute of Science and Technology)
DTSTART:20231225T050000Z
DTEND:20231225T063000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/44
DESCRIPTION:Title: Rigidity of bricks and brick-Brauer-Thrall conjectures
II\nby Kaveh Mousavand (Okinawa Institute of Science and Technology) a
s part of Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale)
DTSTART:20231226T060000Z
DTEND:20231226T073000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/45
DESCRIPTION:Title: t-structures on the equivariant derived category of the
Steinberg scheme\nby Ivan Losev (Yale) as part of Tokyo-Nagoya Algebr
a Seminar\n\n\nAbstract\nThe Steinberg scheme and the equivariant coherent
sheaves on it play a very important role in Geometric Representation theo
ry. In this talk we will discuss various t-structures on the equivariant d
erived category of the Steinberg of importance for Representation theory i
n positive characteristics. Based on arXiv:2302.05782.\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (Tokyo)
DTSTART:20231227T003000Z
DTEND:20231227T040000Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/46
DESCRIPTION:by Osamu Iyama (Tokyo) as part of Tokyo-Nagoya Algebra Seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Tokyo)
DTSTART:20231227T053000Z
DTEND:20231227T084500Z
DTSTAMP:20260404T111416Z
UID:TokyoNagoyaAlgebra/47
DESCRIPTION:Title: Interval neighborhoods of silting cones\nby Sota As
ai (Tokyo) as part of Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TokyoNagoyaAlgebra/47/
END:VEVENT
END:VCALENDAR