BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Yasuaki Gyoda (Nagoya University)
DTSTART:20201027T073000Z
DTEND:20201027T090000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/1
DESCRIPTION:Title: Positive cluster complex and tau-tilting complex\nby Yasuak
i Gyoda (Nagoya University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nA
bstract\nIn cluster algebra theory\, cluster complexes are actively studie
d as simplicial complexes\, which represent the structure of a seed and it
s mutations. In this talk\, I will discuss a certain subcomplex\, called p
ositive cluster complex\, of a cluster complex. This is a subcomplex whose
vertex set consists of all cluster variables except for those in the init
ial seed. I will also introduce another simplicial complex in this talk -
the tau-tilting complex\, which has vertices given by all indecomposable t
au-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\, we can i
nvestigate the structure of a tau-tilting complex of tau-tilting finite ty
pe by using the tools of cluster algebra theory. This is joint work with H
aruhisa Enomoto.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arashi Sakai (Nagoya University)
DTSTART:20201112T070000Z
DTEND:20201112T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/2
DESCRIPTION:Title: ICE-closed subcategories and wide tau-tilting modules\nby A
rashi Sakai (Nagoya University) as part of Tokyo-Nagoya Algebra Seminar\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wid
e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 t
au-tilting 加群を導入し、ICE-closed 部分圏がwide tau-tilting
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://researchseminars.org/talk/TokyoNagoyaAlgebra/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Hirano (Kyoto University)
DTSTART:20201203T070000Z
DTEND:20201203T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/3
DESCRIPTION:Title: Full strong exceptional collections for invertible polynomials
of chain type\nby Yuki Hirano (Kyoto University) as part of Tokyo-Nago
ya Algebra Seminar\n\n\nAbstract\nConstructing a tilting object in the sta
ble category of graded maximal Cohen-Macaulay modules over a given graded
Gorenstein ring is an important problem in the representation theory of gr
aded Gorenstein rings. For a hypersurface S/f in a graded regular ring S\,
this problem is equivalent to constructing a tilting object in the homoto
py category of graded matrix factorizations of f. In this talk\, we discus
s this problem in the case when S is a polynomial ring\, f is an invertibl
e polynomial of chain type and S has a rank one abelian group grading (cal
led the maximal grading of f)\, and in this case we show the existence of
a tilting object arising from a full strong exceptional collection. This i
s a joint work with Genki Ouchi.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Matsui (University of Tokyo)
DTSTART:20201210T073000Z
DTEND:20201210T090000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/4
DESCRIPTION:Title: Subcategories of module or derived categories\, and subsets of
Zariski spectra\nby Hiroki Matsui (University of Tokyo) as part of Tok
yo-Nagoya Algebra Seminar\n\n\nAbstract\nThe classification problem of sub
categories has been well considered in many areas. This problem was initia
ted by Gabriel in 1962 by giving a classification of localizing subcategor
ies of the module category Mod R via specialization-closed subsets of the
Zariski spectrum Spec R for a commutative noetherian ring. After that seve
ral authors tried to generalize this result in many ways. For example\, fo
ur decades later\, Krause introduced the notion of coherent subsets of Spe
c R and used it to classify wide subcategories of Mod R. In this talk\, I
will introduce the notions of n-wide subcategories of Mod R and n-coherent
subsets of Spec R for a (possibly infinite) non-negative integer n. I wil
l also introduce the notion of n-uniform subcategories of the derived cate
gory D(Mod R) and prove the correspondences among these classes. This resu
lt unifies/generalizes many known results such as the classification given
by Gabriel\, Krause\, Neeman\, Takahashi\, Angeleri Hugel-Marks-Stovicek-
Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.\n
LOCATION:https://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:20260422T213052Z
UID:TokyoNagoyaAlgebra/6
DESCRIPTION:Title: The finite EI categories of Cartan type\nby Xiao-Wu Chen (U
niversity of Science and Technology of China) as part of Tokyo-Nagoya Alge
bra Seminar\n\n\nAbstract\nWe will recall the notion of a finite free EI c
ategory introduced by Li. To each Cartan triple\, we associate a finite fr
ee EI category\, called the finite EI category of Cartan type. The corresp
onding category algebra is isomorphic to the 1-Gorenstein algebra\, introd
uced by Geiss-Leclerc-Schroer\, which is associated to possibly another Ca
rtan triple. The construction of the second Cartan triple is related to th
e well-known unfolding of valued graphs. We will apply the obtained algebr
a isomorphism to re-interpret some tau-locally free modules as induced mod
ules over a certain skew group algebra. This project is joint with Ren Wan
g.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Ohkawa (Kobe University)
DTSTART:20210114T070000Z
DTEND:20210114T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/7
DESCRIPTION:Title: (-2) blow-up formula\nby Ryo Ohkawa (Kobe University) as pa
rt 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://researchseminars.org/talk/TokyoNagoyaAlgebra/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hideya Watanabe (RIMS\, Kyoto University)
DTSTART:20210121T080000Z
DTEND:20210121T093000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/8
DESCRIPTION:Title: Based modules over the $\\imath$-quantum group of type AI\n
by Hideya Watanabe (RIMS\, Kyoto University) as part of Tokyo-Nagoya Algeb
ra Seminar\n\n\nAbstract\nIn recent years\, $\\imath$-quantum groups are i
ntensively studied because of their importance in various branches of math
ematics and physics. Although $\\imath$-quantum groups are thought of as
generalizations of Drinfeld-Jimbo quantum groups\, their representation th
eory is much more difficult than that of quantum groups. In this talk\, I
will focus on the $\\imath$-quantum group of type AI. It is a non-standar
d quantization of the special orthogonal Lie algebra $\\mathfrak{so}_n$.
I will report my recent research on based modules\, which are modules equi
pped with distinguished bases\, called the $\\imath$-canonical bases. The
first main result is a new combinatorial formula describing the branching
rule from $\\mathfrak{sl}_n$ to $\\mathfrak{so}_n$. The second one is th
e irreducibility of cell modules associated with the $\\\\imath$-canonical
bases.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akishi Ikeda (Josai University)
DTSTART:20210210T070000Z
DTEND:20210210T083000Z
DTSTAMP:20260422T213052Z
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-Nagoya
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-Katzark
ov-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Jacobi
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://researchseminars.org/talk/TokyoNagoyaAlgebra/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunya Saito (Nagoya University)
DTSTART:20210224T070000Z
DTEND:20210224T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/10
DESCRIPTION:Title: 周期三角圏上の傾理論\nby Shunya Saito (Nagoya Un
iversity) 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://researchseminars.org/talk/TokyoNagoyaAlgebra/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akihito Wachi (Hokkaido University of Education)
DTSTART:20210311T070000Z
DTEND:20210311T083000Z
DTSTAMP:20260422T213052Z
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 Educat
ion) 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://researchseminars.org/talk/TokyoNagoyaAlgebra/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (University of Sydney)
DTSTART:20210408T070000Z
DTEND:20210408T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/12
DESCRIPTION:Title: Abelian envelopes of monoidal categories\nby Kevin Coulemb
ier (University of Sydney) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAb
stract\nFor the purposes of this talk\, a ‘tensor category’ is an abel
ian 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 tensor cat
egories to non-abelian rigid monoidal categories. Then I will comment on s
ome of the recent progress made on such constructions (in work of Benson\,
Comes\, Entova\, Etingof\, Heidersdof\, Hinich\, Ostrik\, Serganova and m
yself).\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Külshammer (Uppsala University)
DTSTART:20210422T070000Z
DTEND:20210422T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/13
DESCRIPTION:Title: Exact categories via $A_\\infty$-algebras\nby Julian Küls
hammer (Uppsala University) as part of Tokyo-Nagoya Algebra Seminar\n\n
\nAbstract\nMany instances of extension closed subcategories appear throug
hout representation theory\, e.g. filtered modules\, Gorenstein projective
s\, as well as modules of finite projective dimension. In the first part o
f the talk\, I will outline a general strategy to realise such subcategori
es as categories of induced modules from a subalgebra using $A_\\infty$-al
gebras. In the second part\, I will describe how this strategy has been su
ccessfully applied for the exact category of filtered modules over a quasi
hereditary algebra. In particular I will present compatibility results of
this approach with heredity ideals in a quasihereditary algebra from joint
work with Teresa Conde.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Charles University)
DTSTART:20210506T070000Z
DTEND:20210506T083000Z
DTSTAMP:20260422T213052Z
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\nAbstract
\nIt is well known that if A is a Cohen-Macaulay ring and $a_1\,\\dots\,a_
n$ is an $A$-regular sequence\, then the quotient ring $A/(a_1\,\\dots\,a_
n)$ is also a Cohen-Macaulay ring. In this talk we explain that by derivin
g 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 $A$ wit
h respect to $(a_1\,\\dots\,a_n)$ is Cohen-Macaulay. Several applications
of this result are given\, including a generalization of Hironaka's miracl
e flatness theorem to derived algebraic geometry.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Kanda (Osaka City University)
DTSTART:20210520T070000Z
DTEND:20210520T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/15
DESCRIPTION:Title: Flat cotorsion modules over Noether algebras\nby Ryo Kanda
(Osaka City University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbst
ract\nThis talk is based on joint work with Tsutomu Nakamura. For a module
-finite algebra over a commutative noetherian ring\, we give a complete de
scription of flat cotorsion modules in terms of prime ideals of the algebr
a\, as a generalization of Enochs' result for a commutative noetherian rin
g. As a consequence\, we show that pointwise Matlis duality gives a biject
ive correspondence between the isoclasses of indecomposable flat cotorsion
right modules and the isoclasses of indecomposable injective left modules
. This correspondence is an explicit realization of Herzog's homeomorphism
induced from elementary duality between Ziegler spectra.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Murai (Waseda University)
DTSTART:20210602T070000Z
DTEND:20210602T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/16
DESCRIPTION:Title: An equivariant Hochster's formula for $S_n$-invariant monomial
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Hoc
hster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$\\beta_{ij}(I)=\\dim_K \\mathrm{Tor
}_i(I\,K)_j$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(Noetheriani
ty 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://researchseminars.org/talk/TokyoNagoyaAlgebra/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kohei Kikuta (Chuo University)
DTSTART:20210624T070000Z
DTEND:20210624T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/17
DESCRIPTION:Title: Rank 2 free subgroups in autoequivalence groups of Calabi-Yau
categories\nby Kohei Kikuta (Chuo University) as part of Tokyo-Nagoya
Algebra Seminar\n\n\nAbstract\nVia homological mirror symmetry\, there is
a relation between autoequivalence groups of derived categories of coheren
t sheaves on Calabi-Yau varieties\, and the symplectic mapping class group
s of symplectic manifolds. In this talk\, as an analogue of mapping class
groups of closed oriented surfaces\, we study autoequivalence groups of Ca
labi-Yau triangulated categories. In particular\, we consider embeddings o
f rank 2 (non- commutative) free groups generated by spherical twists. 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://researchseminars.org/talk/TokyoNagoyaAlgebra/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsukasa Ishibashi (RIMS\, Kyoto University)
DTSTART:20210708T070000Z
DTEND:20210708T083000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/18
DESCRIPTION:Title: Sign-stable mutation loops and pseudo-Anosov mapping classes\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://researchseminars.org/talk/TokyoNagoyaAlgebra/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kozakai (Tokyo Science University)
DTSTART:20211119T080000Z
DTEND:20211119T093000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/19
DESCRIPTION:Title: 有限群のブロック上の$\\tau$-傾理論\nby Yuta K
ozakai (Tokyo Science University) as part of Tokyo-Nagoya Algebra Seminar\
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://researchseminars.org/talk/TokyoNagoyaAlgebra/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Cologne)
DTSTART:20211216T074500Z
DTEND:20211216T091500Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/20
DESCRIPTION:Title: Cyclic polytopes and higher Auslander-Reiten theory\nby Ni
cholas Williams (University of Cologne) as part of Tokyo-Nagoya Algebra Se
minar\n\n\nAbstract\nOppermann and Thomas show that tilting modules over I
yama’s higher\nAuslander algebras of type A are in bijection with triang
ulations of\neven-dimensional cyclic polytopes. Triangulations of cyclic p
olytopes\nare partially ordered in two natural ways known as the higher\nS
tasheff-Tamari orders\, which were introduced in the 1990s by\nKapranov\,
Voevodsky\, Edelman\, and Reiner as higher-dimensional\ngeneralisations of
the Tamari lattice. These two partial orders were\nconjectured to be equa
l in 1996 by Edelman and Reiner\, and we prove\nthat this conjecture is tr
ue. \n\nWe further show how the higher\nStasheff-Tamari orders correspond
in even dimensions to natural orders\non tilting modules which were studie
d by Riedtmann\, Schofield\, Happel\,\nand Unger. This then allows us to c
omplete the picture of Oppermann\nand Thomas by showing that triangulation
s of odd-dimensional cyclic\npolytopes correspond to equivalence classes o
f d-maximal green\nsequences\, which we introduce as higher-dimensional an
alogues of\nKeller’s maximal green sequences. We show that the higher\nS
tasheff-Tamari orders correspond to natural orders on equivalence\nclasses
of d-maximal green sequences\, which relate to the no-gap\nconjecture of
Brustle\, Dupont\, and Perotin. The equality of the higher\nStasheff-Tamar
i orders then implies that these algebraic orders on\ntilting modules and
d-maximal green sequences are equal. If time\npermits\, we will also discu
ss some results on mutation of\ncluster-tilting objects and triangulations
.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Prefecture University)
DTSTART:20220118T060000Z
DTEND:20220118T073000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/21
DESCRIPTION:Title: Exact-categorical properties of subcategories of abelian categ
ories\nby Haruhisa Enomoto (Osaka Prefecture University) as part of To
kyo-Nagoya Algebra Seminar\n\n\nAbstract\nQuillen's exact category is a po
werful framework for studying extension-closed subcategories of abelian ca
tegories\, and provides many interesting questions on such subcategories.
In the first talk\, I will explain the basics of some properties and invar
iants of exact categories (e.g. the Jordan-Holder property\, simple object
s\, and Grothendieck monoid). In the second talk\, I will give some result
s and questions about particular classes of exact categories arising in th
e representation theory of algebras (e.g. torsion(-free) classes over path
algebras and preprojective algebras). If time permits\, I will discuss qu
estions of whether these results can be generalized to extriangulated cate
gories (extension-closed subcategories of triangulated categories).\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Prefecture University)
DTSTART:20220121T074500Z
DTEND:20220121T091500Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/22
DESCRIPTION:Title: Exact-categorical properties of subcategories of abelian categ
ories 2\nby Haruhisa Enomoto (Osaka Prefecture University) as part of
Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nQuillen's exact category is a
powerful framework for studying extension-closed subcategories of abelian
categories\, and provides many interesting questions on such subcategories
. In the first talk\, I will explain the basics of some properties and inv
ariants of exact categories (e.g. the Jordan-Holder property\, simple obje
cts\, and Grothendieck monoid). In the second talk\, I will give some resu
lts and questions about particular classes of exact categories arising in
the representation theory of algebras (e.g. torsion(-free) classes over pa
th algebras and preprojective algebras). If time permits\, I will discuss
questions of whether these results can be generalized to extriangulated ca
tegories (extension-closed subcategories of triangulated categories).\n\nT
his talk is the second half of the lecture series.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigeo Koshitani (Chiba University)
DTSTART:20220309T040000Z
DTEND:20220309T053000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/23
DESCRIPTION:Title: Modular representation theory of finite groups – local versu
s global\nby Shigeo Koshitani (Chiba University) as part of Tokyo-Nago
ya Algebra Seminar\n\n\nAbstract\nWe are going to talk about representatio
n theory of finite groups. In the 1st part it will be on "Equivalences of
categories ” showing up for block theory in modular representation theor
y\, 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 kind of local—gl
obal conjectures in modular representation theory of finite groups\, that
originally and essentially are due to Richard Brauer (1901–77).\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shigeo Koshitani (Chiba University)
DTSTART:20220311T040000Z
DTEND:20220311T053000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/24
DESCRIPTION:Title: Modular representation theory of finite groups – local versu
s global (part 2)\nby Shigeo Koshitani (Chiba University) as part of T
okyo-Nagoya Algebra Seminar\n\n\nAbstract\nWe are going to talk about repr
esentation theory of finite groups. In the 1st part it will be on "Equival
ences of categories ” showing up for block theory in modular representat
ion theory\, and it should be kind of introductory lecture/talk. So the au
dience 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 l
ocal—global conjectures in modular representation theory of finite group
s\, that originally and essentially are due to Richard Brauer (1901–77).
\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Osaka Metropolitan University)
DTSTART:20220413T013000Z
DTEND:20220413T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/25
DESCRIPTION:Title: Tilting ideals of deformed preprojective algebras\nby Yuta
Kimura (Osaka Metropolitan University) as part of Tokyo-Nagoya Algebra Se
minar\n\n\nAbstract\nLet $K$ be a field and $Q$ a finite quiver.\nFor a we
ight $\\lambda \\in K^{|Q_0|}$\, the deformed preprojective\nalgebra $\\Pi
^{\\lambda}$ was introduced by Crawley-Boevey and Holland\nto study deform
ations of Kleinian singularities.\nIf $\\lambda = 0$\, then $\\Pi^{0}$ is
the preprojective algebra\nintroduced by Gelfand-Ponomarev\, and appears m
any areas of\nmathematics.\nAmong interesting properties of $\\Pi^{0}$\, t
he classification of\ntilting ideals of $\\Pi^{0}$\, shown by Buan-Iyama-R
eiten-Scott\, is\nfundamental and important.\nThey constructed a bijection
between the set of tilting ideals of\n$\\Pi^{0}$ and the Coxeter group $W
_Q$ 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 exists a bij
ection between\ntilting ideals and a Coxeter group.\nHowever $W_Q$ does no
t appear\, since $\\Pi^{\\lambda}$ is not necessary basic.\nInstead of $W_
Q$\, we consider the Ext-quiver of rigid simple modules\,\nand use its Cox
eter group.\nWhen $Q$ is an extended Dynkin quiver\, we see that the Ext-q
uiver is\nfinite and this has an information of singularities of a\nrepres
entation space of semisimple modules.\nThis is joint work with William Cra
wley-Boevey.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiko Yoshinaga (Osaka University)
DTSTART:20220601T013000Z
DTEND:20220601T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/26
DESCRIPTION:Title: 超平面配置の特性準多項式\nby Masahiko Yoshinag
a (Osaka University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract
\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://researchseminars.org/talk/TokyoNagoyaAlgebra/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiko Yoshinaga (Osaka University)
DTSTART:20220608T013000Z
DTEND:20220608T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/27
DESCRIPTION:Title: 超平面配置の特性準多項式\nby Masahiko Yoshinag
a (Osaka University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract
\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://researchseminars.org/talk/TokyoNagoyaAlgebra/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (Freiburg University)
DTSTART:20220622T080000Z
DTEND:20220622T093000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/28
DESCRIPTION:Title: Update on singular equivalences between commutative rings\
nby Martin Kalck (Freiburg University) as part of Tokyo-Nagoya Algebra Sem
inar\n\n\nAbstract\nWe will start with an introduction to singularity cate
gories\, which\n were first studied by Buchweitz and later rediscov
ered by Orlov.\n Then we will explain what is known about triangle
equivalences between\n singularity categories of commutative rings\
, recalling results of\n Knörrer\, D. Yang (based on our joint wor
ks on relative singularity\n categories. This result also follows f
rom work of Kawamata and was\n generalized in a joint work with Kar
mazyn) 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 Gorenstei
n\n isolated singularities and especially hypersurfaces\, where we
give a\n complete description of quasi-equivalence classes of dg en
hancements\n of singularity categories\, answering a question of Ke
ller & Shinder.\n This is based on arXiv:2108.03292.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220615T013000Z
DTEND:20220615T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/29
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 1\nby
Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Algebra S
eminar\n\n\nAbstract\nIn this series of three talks\, we expand upon the p
revious talk (see attached link to the slides) given\nat the seminar and s
tudy the relationship between cyclic polytopes and\nhigher Auslander--Reit
en theory in more detail.\n\nIn the first talk\, we focus on cyclic polyto
pes. We survey important\nproperties of cyclic polytopes\, such as differe
nt ways to construct\nthem\, the Upper Bound Theorem\, and their Ramsey-th
eoretic properties.\nWe then move on to triangulations of cyclic polytopes
. We give\nefficient combinatorial descriptions of triangulations of\neven
-dimensional and odd-dimensional cyclic polytopes\, which we will\nuse in
subsequent talks. We finally define the higher Stasheff--Tamari\norders on
triangulations of cyclic polytopes. We give important\nresults on the ord
ers\, including Rambau's Theorem\, and the equality of\nthe two orders.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220629T013000Z
DTEND:20220629T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/30
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 2\nby
Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Algebra S
eminar\n\n\nAbstract\nIn the second talk\, we focus on higher Auslander--R
eiten theory. We survey the basic setting of this theory\, starting with d
-cluster-tilting subcategories of module categories. We then move on to d-
cluster-tilting subcategories of derived categories in the case of d-repre
sentation-finite d-hereditary algebras. We explain how one can construct (
d + 2)-angulated cluster categories for such algebras\, generalising class
ical cluster categories. We finally consider the d-almost positive categor
y\, which is the higher generalisation of the category of two-term complex
es. Throughout\, we illustrate the results using the higher Auslander alge
bras of type A\, and explain how the different categories can be interpret
ed combinatorially for these algebras.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (University of Tokyo)
DTSTART:20220706T013000Z
DTEND:20220706T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/31
DESCRIPTION:Title: Cyclic polytopes and higher Auslander--Reiten theory 3\nby
Nicholas Williams (University of Tokyo) as part of Tokyo-Nagoya Algebra S
eminar\n\n\nAbstract\nIn the third talk\, we consider the relationship bet
ween the objects from the first two talks. We explain how triangulations o
f even-dimensional cyclic polytopes may be interpreted in terms of tilting
modules\, cluster-tilting objects\, or d-silting complexes. We then proce
ed in the d-silting framework\, and show how the higher Stasheff--Tamari o
rders may be interpreted algebraically for even dimensions. We explain how
this allows one to interpret odd-dimensional triangulations algebraically
\, namely\, as equivalence classes of d-maximal green sequences. We briefl
y digress to consider the issue of equivalence of maximal green sequences
itself. We then show how one can interpret the higher Stasheff--Tamari ord
ers on equivalence classes of d-maximal green sequences. We finish by draw
ing out some consequences of this algebraic interpretation of the higher S
tasheff--Tamari orders.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Imamura (Osaka University)
DTSTART:20220720T013000Z
DTEND:20220720T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/32
DESCRIPTION:Title: Grothendieck enriched categories\nby Yuki Imamura (Osaka U
niversity) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nGrothend
ieck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Gr
othendieck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://researchseminars.org/talk/TokyoNagoyaAlgebra/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck (Freiburg University)
DTSTART:20221020T074000Z
DTEND:20221020T091000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/33
DESCRIPTION:Title: A surface and a threefold with equivalent singularity categori
es\nby Martin Kalck (Freiburg University) as part of Tokyo-Nagoya Alge
bra Seminar\n\n\nAbstract\nWe discuss a triangle equivalence between singu
larity categories of an affine surface and an affine threefold. Both are i
solated cyclic quotient singularities. This seems to be the first (non-tri
vial) example of a singular equivalence involving varieties of even and od
d Krull dimension.\n\nThe same approach recovers a result of Dong Yang sho
wing a singular equivalence between certain cyclic quotient singularities
in dimension 2 and certain finite dimensional commutative algebras.\n\nThi
s talk is based on https://arxiv.org/pdf/2103.06584.pdf\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunske Kano (Tohoku University)
DTSTART:20230120T013000Z
DTEND:20230120T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/34
DESCRIPTION:Title: Tropical cluster transformations and train track splittings\nby Shunske Kano (Tohoku University) as part of Tokyo-Nagoya Algebra Sem
inar\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://researchseminars.org/talk/TokyoNagoyaAlgebra/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (University of Glasgow)
DTSTART:20230220T080000Z
DTEND:20230220T093000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/35
DESCRIPTION:Title: Silting discrete代数上のsemibrick複体とspherical object
s\nby Wahei Hara (University of Glasgow) as part of Tokyo-Nagoya Algeb
ra 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「silting
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contra
ction 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Kleinian
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://researchseminars.org/talk/TokyoNagoyaAlgebra/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kota Murakami (Tokyo University)
DTSTART:20230421T040000Z
DTEND:20230421T053000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/36
DESCRIPTION:Title: Categorifications of deformed Cartan matrices\nby Kota Mur
akami (Tokyo University) as part of Tokyo-Nagoya Algebra Seminar\n\n\nAbst
ract\nIn a series of works of Geis-Leclerc-Schroer\, they introduced a ver
sion of preprojective algebra associated with a symmetrizable generalized
Cartan matrix and its symmetrizer. For finite type\, it can be regarded as
an un-graded analogue of Jacobian algebra of certain quiver with potentia
l appeared in the theory of (monoidal) categorification of cluster algebra
s.\n\nIn this talk\, we will present an interpretation of graded structure
s of the preprojective algebra of general type\, in terms of a multi-param
eter deformation of generalized Cartan matrix and relevant combinatorics m
otivated from several contexts in the theory of quantum loop algebras or q
uiver $\\mathcal{W}$-algebras. From the vantage point of the representatio
n theory of preprojective algebra\, we will prove several purely combinato
rial properties of these concepts. This talk is based on a joint work with
Ryo Fujita (RIMS).\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takumi Otani (Osaka University)
DTSTART:20230428T040000Z
DTEND:20230428T053000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/37
DESCRIPTION:Title: Full exceptional collections associated with Bridgeland stabil
ity conditions\nby Takumi Otani (Osaka University) as part of Tokyo-Na
goya Algebra Seminar\n\n\nAbstract\nThe space of Bridgeland stability cond
itions on a triangulated category is important in mirror symmetry and many
people develop various techniques to study it. In order to study the homo
topy type of the space of stability conditions\, Macri studied stability c
onditions associated with full exceptional collections. Based on his work\
, Dimitrov-Katzarkov introduced the notion of a full σσ-exceptional coll
ection for a stability condition σσ.\n\nIn this talk\, I will explain th
e relationship between full exceptional collections and stability conditio
ns and some properties. I will also talk about the existence of full σσ-
exceptional collections for the derived category of an acyclic quiver.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine de Saint Germain (University of Hong Kong)
DTSTART:20230516T060000Z
DTEND:20230516T073000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/38
DESCRIPTION:Title: Cluster-additive functions and frieze patterns with coefficien
ts\nby Antoine de Saint Germain (University of Hong Kong) as part of T
okyo-Nagoya Algebra Seminar\n\n\nAbstract\nIn his study of combinatorial f
eatures of cluster categories and cluster-tilted algebras\, Ringel introdu
ced an analogue of additive functions of stable translation quivers called
cluster-additive functions.\n\nIn the first part of this talk\, we will d
efine cluster-additive functions associated to any acyclic mutation matrix
\, relate them to mutations of the cluster X variety\, and realise their v
alues as certain compatibility degrees between functions on the cluster A
variety associated to the Langlands dual mutation matrix (in accordance wi
th the philosophy of Fock-Goncharov). This is based on joint work with Pei
gen Cao and Jiang-Hua Lu. In the second part of this talk\, we will introd
uce the notion of frieze patterns with coefficients based on joint work wi
th Min Huang and Jiang-Hua Lu. We will then discuss their connection with
cluster-additive functions.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hideto Asashiba
DTSTART:20230707T060000Z
DTEND:20230707T073000Z
DTSTAMP:20260422T213052Z
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 part of To
kyo-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://researchseminars.org/talk/TokyoNagoyaAlgebra/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART:20230714T013000Z
DTEND:20230714T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/40
DESCRIPTION:Title: Local Forms of Noncommutative Functions and Applications\n
by Michael Wemyss (University of Glasgow) as part of Tokyo-Nagoya Algebra
Seminar\n\n\nAbstract\nThis talk will explain how Arnold's results for com
mutative\nsingularities can be extended into the noncommutative setting\,
with\nthe main result being a classification of certain Jacobi algebras\na
rising from (complete) free algebras. This class includes finite\ndimensio
nal Jacobi algebras\, and also Jacobi algebras of GK dimension\none\, suit
ably interpreted. The surprising thing is that a\nclassification should ex
ist at all\, and it is even more surprising\nthat ADE enters.\n\nI will sp
end most of my time explaining what the algebras are\, what\nthey classify
\, and how to intrinsically extract ADE information from\nthem. At the end
\, I'll explain why I'm really interested in this\nproblem\, an update inc
luding results on different quivers\, and the\napplications of the above c
lassification to curve counting and\nbirational geometry. This is joint wo
rk with Gavin Brown.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Ren (Kansai University)
DTSTART:20231012T013000Z
DTEND:20231012T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/41
DESCRIPTION:Title: $q$-deformed rational numbers\, Farey sum and a 2-Calabi-Yau c
ategory of $A_2$ quiver\nby Xin Ren (Kansai University) as part of
Tokyo-Nagoya Algebra Seminar\n\n\nAbstract\nLet $q$ be a positive real num
ber. The left and right $q$-deformed rational numbers were introduced by B
apat\, Becker and Licata via regular continued fractions\, and the right $
q$-deformed rational number is exactly $q$-deformed rational number consid
ered by Morier-Genoud and Ovsienko\, when $q$ is a formal parameter. They
gave a homological interpretation for left and right $q$-deformed rational
numbers by considering a special 2-Calabi–Yau category associated to th
e $A_2$ quiver.\n\nIn this talk\, we begin by introducing the above defini
tions and related results. Then we give a formula for computing the $q$-de
formed Farey sum of the left $q$-deformed rational numbers based on the ne
gative continued fractions. We combine the homological interpretation of t
he left and right $q$-deformed rational numbers and the $q$-deformed Farey
sum\, and give a homological interpretation of the $q$-deformed Farey sum
. We also apply the above results to real quadratic irrational numbers wit
h periodic type.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (University of Science and Technology of China)
DTSTART:20231214T013000Z
DTEND:20231214T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/42
DESCRIPTION:Title: On exact dg categories\nby Xiaofa Chen (University of Scie
nce and Technology of China) as part of Tokyo-Nagoya Algebra Seminar\n\n\n
Abstract\nIn this talk\, I will give an introduction to exact dg categorie
s and then explore their application to various correspondences in represe
ntation theory. We will generalize the Auslander–Iyama correspondence\,
the Iyama–Solberg correspondence\, and a correspondence considered in a
paper by Iyama in 2005 to the setting of exact dg categories. The slogan i
s that solving correspondence-type problems becomes easier using dg catego
ries\, and interesting phenomena emerge when the dg category is concentrat
ed in degree zero or is abelian.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (Okinawa Institute of Science and Technology)
DTSTART:20231225T013000Z
DTEND:20231225T030000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/43
DESCRIPTION:Title: Rigidity of bricks and brick-Brauer-Thrall conjectures I\n
by Kaveh Mousavand (Okinawa Institute of Science and Technology) as part o
f Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (Okinawa Institute of Science and Technology)
DTSTART:20231225T050000Z
DTEND:20231225T063000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/44
DESCRIPTION:Title: Rigidity of bricks and brick-Brauer-Thrall conjectures II\
nby Kaveh Mousavand (Okinawa Institute of Science and Technology) as part
of Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Losev (Yale)
DTSTART:20231226T060000Z
DTEND:20231226T073000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/45
DESCRIPTION:Title: t-structures on the equivariant derived category of the Steinb
erg scheme\nby Ivan Losev (Yale) as part of Tokyo-Nagoya Algebra Semin
ar\n\n\nAbstract\nThe Steinberg scheme and the equivariant coherent sheave
s on it play a very important role in Geometric Representation theory. In
this talk we will discuss various t-structures on the equivariant derived
category of the Steinberg of importance for Representation theory in posit
ive characteristics. Based on arXiv:2302.05782.\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (Tokyo)
DTSTART:20231227T003000Z
DTEND:20231227T040000Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/46
DESCRIPTION:by Osamu Iyama (Tokyo) as part of Tokyo-Nagoya Algebra Seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Tokyo)
DTSTART:20231227T053000Z
DTEND:20231227T084500Z
DTSTAMP:20260422T213052Z
UID:TokyoNagoyaAlgebra/47
DESCRIPTION:Title: Interval neighborhoods of silting cones\nby Sota Asai (Tok
yo) as part of Tokyo-Nagoya Algebra Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TokyoNagoyaAlgebra/47/
END:VEVENT
END:VCALENDAR