Tsukuba Repository  (Tulips-R)

筑波大学大学院人間総合科学学術院人間総合科学研究群 芸術学学位プログラム（博士前期課程）カリキュラム委員会

Japanese

The Synopses of Master’s Theses, Master’s Program in Art, 2023

橋本 康二

Christine Ladd-Franklin and Wittgenstein’s Tractatus

橋本 陸

和久田 高之

<School Research 2>Practical Study on How It Should Be to Teach Arithmetic Mathematics to Children with Intellectual and Physical Disabilities: Designing Lesson Plans to Make Children Immersed in “the World of Mathematics”

95
研究活動報告
三宅　裕　トルコ・チャクマックテペ遺跡の発掘調査 .「第 30 回西アジア発掘調査報告会の開催にあたっ
て」『第 30 回西アジア発掘調査報告会報告集：令和 4 年度考古学が語る古代オリエント』.  「石灰岩の丘に
暮らした狩猟採集民―トルコ，チャクマックテペ遺跡，第 2 次調査（2022 年）」『第 30 回西アジア発掘調
査報告会報告集：令和 4 年度考古学が語る古代オリエント』.「西アジア新石器時代における社会システム
の転換」『岩波講座世界歴史 2 古代西アジアとギリシア～前１世紀』.「石灰岩の丘に暮らした狩猟採集民―
トルコ，チャクマックテペ遺跡，第 2 次調査（2022 年）」『第 30 回西アジア発掘調査報告会』（口頭発表）. 
Faunal remains from Salat Cami Yanı: An Early Pottery Neolithic site in the Upper Tigris Valley. Animals and humans 
through time and space: Investigating diverse relationships.（共著）.  Communal buildings and social complexity in 
the Neolithic Southwest Asia. Cities and Urbanization in West Asia and Egypt: Shapes, functions, and ideology.（口
頭発表）.
滝沢　誠　静岡県西伊豆町辰ケ口岩陰遺跡出土遺物の調査．静岡県下田市上ノ山洞穴遺跡の発掘調査．茨
城県土浦市常名天神山古墳の測量・発掘調査．『王塚古墳・后塚古墳―土浦市教育委員会・筑波大学考古学
研究室合同発掘調査報告書―』土浦市教育委員会（共編著）．「中期の甲冑 2：帯金式短甲」『季刊考古学』
165．「伊豆半島南部の古墳時代洞穴墓―下田市了仙寺洞穴・上ノ山洞穴の測量調査」『筑波大学先史学・考
古学研究』34（共著）．「愛鷹山に眠る開拓者たち」『富士市内遺跡発掘調査報告書―令和 3 年度―』富士市
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塚古墳・后塚古墳と霞ケ浦周辺の前期古墳」『上高津貝塚ふるさと歴史の広場第 26 回企画展記念講演会　
霞ケ浦の前期古墳と地域社会の成り立ち』（講演・シンポジウム）．
谷口　陽子　大エジプト博物館合同保存修復プロジェクト（壁画）（JICA）．シリア・アラブ共和国におけ
るアイン・ダーラ遺跡の保護のための人材育成事業（文化庁）．トルコ・カッパドキア，聖シメオン遺跡の
保存修復・調査プロジェクト．アフガニスタン，ストゥッコ像の技法材料調査（科研）.  Scientific Studies on 
Conservation for Saint Simeon Church and Its Wall Paintings in Cappadocia, Turkey: Vol.1 (Report on the activities in 
2019 and 2022), University of Tsukuba.「先史学実習 - C における毛織物（キリム）の放射性炭素年代測定」『筑
波大学 先史学・考古学研究』34（共著）.「（3）茨城県指定有形文化財考古資料　考第 32 号　堀米 A 遺跡
出土硬玉製大珠 5 点」『茨城の文化財　第 61 集』.「目梨泊遺跡（北海道枝幸町）出土オホーツク時代の刀
装具の技法材料分析からみえる東・北東アジアのグローバル交易」『2023 東アジア文化遺産保存国際シン
ポジウム in 札幌』（口頭発表）.「世界遺産カッパドキア・聖シメオン教会の壁画の保存修復：ヴァンダリズ
ムに対するアプローチ」『文化財保存修復学会第 45 回大会』（ポスター発表）.「月崇寺（茨城県笠間市）所
蔵の鎌倉時代来迎図の彩色について」『文化財科学会第 40 回大会　彩色材料分析 WG』（口頭発表）.「古代
から中世の彩色技法と材料 : 西アジア，地中海，中央アジアから日本」『古代ギリシア彫刻と彩色』（口頭
発表）.
前田　修　イラク・クルディスタン，シャカル・テペ遺跡の発掘調査．「新石器化と都市化のはざま─シャ
イフ・マリフ遺跡の第 1 次発掘調査（2022 年）─」『考古学が語る古代オリエント 第 30 回西アジア発掘
調査報告会報告集』（共著）．Excavations at Shaikh Marif, Iraqi Kurdistan Preliminary Report of the First Season 
(2022). Ancient Civilizations and Cultural Resources, 1（共著）．Late Prehistoric Investigations at Shakar Tepe, the 
Shahrizor Plain, Iraqi Kurdistan: Preliminary Results of the First Season (2019). Proceedings of the 12th International 
Congress on the Archaeology of the Ancient Near East,（共著）．「新石器化と都市化のはざま―イラク・クルデ
ィスタン，シャイフ・マリフ遺跡の第 1 次発掘調査（2022 年）―」『第 30 回西アジア発掘調査報告会』（口
頭発表）．Interactions between Prehistoric Communities and Raw Materials in the Near East. International Obsidian 
Conference (IOC) Engaru 2023（口頭発表）．
板橋　悠　「先史学実習- Cにおける毛織物（キリム）の放射性炭素年代測定」『筑波大学 先史学・考古学研究』
34.（共著）．Reconstruction of diets based on the Δ15N values of individual amino acids at three sites in Sichuan, 
96
China. Archaeometry, 65/4（共著）．「バハレーン古墳埋葬人骨の出自推定とオアシス水の酸素同位体比マッ
プ」『第 2 回 TRiSTAR 共創リレーセミナー』（口頭発表）．「遺跡から見つけた骨を分析して，古代の食生活
を明らかにする」『第 13 回同位体環境学シンポジウム』（ポスター発表）．Feeding marine resources to dogs at 
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Council for Archaeozoology Conference（口頭発表）．
Dana Alnafouri　3D Modelling and Visual Documentation Methods: Showcasing Neolithic Art from Turkey. 
The International Conference on Cultural Heritage and New Technologies, CHNT-ICOMOS Austria, Vienna 15-17 
November 2023（口頭発表）. Preserving Syrian Cultural Diversity and Identity Digital Techniques for Cultural Heritage 
Preservation Education. The International Conference on Cultural Heritage and New Technologies, CHNT-ICOMOS 
Austria, Vienna 15-17 November 2023（口頭発表）．
朱　独伊　研究課題：考古学及び自然科学的手法に基づく中国の墓磚資料の材料・技術研究
平林　大樹　「古墳時代研究の動向」『日本考古学年報』75.『さらしな はにしなの小さな古墳たち』森将軍
塚古墳館千曲市誕生 20 周年記念夏季企画展解説リーフレット . 「連載日本遺産をめぐる第 20 回 月の都 千
曲－姨捨の棚田がつくる摩訶不思議な月景色な月景色「田毎の月」－」『月刊文化財』717.「弥生時代 中部」『考
古学ジャーナル』782.「木島平村根塚遺跡割竹形木棺墓出土遺物の再検討」『横断研究会』（口頭発表）.「長
野県青木下遺跡出土鉄鏃の再検討」『横断研究会』（口頭発表）
王　辰陽　研究課題：中国漢王朝とその以前の青銅器の利用 . 弥生時代の日本に伝入した中国鏡 .
鎌田　涼　「常陸中部の外海沿いにおける古墳時代後期の 5 遺跡で出土したガラス小玉の蛍光 X 線分析」『日
本文化財科学会第 40 回記念大会』（ポスター発表）．
河合　るな　研究課題：西アジア先土器新石器時代における動物シンボルの集成・検討
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山根　萌々花　「中央アジアにおける「飾られた仏陀」と支配者」『筑波大学先史学・考古学研究』34．「東
海村・堀米 A 遺跡出土ヒスイ製大珠の蛍光Ｘ線分析および 3 次元計測」『筑波大学先史学・考古学研究』34（共
著）.
97
令和５年度卒業論文・修士論文一覧
卒業論文
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松下　杏奈　　「江戸時代の化粧道具　―紅皿・紅猪口の検討―」
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三堀乃利行　　「東京教育大学第１次イラン調査隊表採ガラス片資料の分析と検討」
中村　愛美　　「モンゴル帝国期の食生活について」
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田頭　優花　　「縄文時代中期北関東における人の移動　―阿玉台式・大木式土器を中心に―」
宮木　圭太　　「縄文時代および弥生時代におけるサメ歯関連製品の利用について」
松本　琉那　　「埴輪に付属する鳥形土製品の性格」
山本　佳奈　　「弥生再葬墓における土器の系統と造営集団」
高橋　和泉　　「日本におけるパブリック・アーケオロジーの現状と今後への提言」
修士論文
王　　辰陽　　「弥生時代における銅釧の再加工・再利用行為について」


研究活動報告

内山 咲良

窪田 辰政

<Reports>Report on a special lecture at a prefectural university in 2023: Reflection on my university life

坂上 輝将

<Reports>Report on 31th FISU World University Games Water Polo

大学体育研究 46号 : 表紙, 目次, 奥付, 他

星野 豊

教育と法（第182回）生徒の自殺に関する担任への処分の違法性（下）

NISHIMURA Hirokazu

Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin; Park, Euiyong
Affinizations, R-matrices and reflection functors. (English)
  Zbl 07829728
Adv. Math. 443, Article ID 109598, 83 p. (2024)
Affinizations and R-matrices are one of the most powerful tools in the representation theory of quiver
Hecke algebras and affine quantum groups. R-matrices are distinguished homomorphisms between tensor
products of modules, which measure the commutativity of tensor products. Affinizations of modules
help R-matrices to play their role. The study on affinizations and R-matrices gives rise to the integer
invariants Λ, Λ̃ and d, which have been used crucially in deriving several remarkable results including
monoidal categorification of cluster algebras [S.-J. Kang et al., Compos. Math. 151, No. 2, 377–396 (2015;
Zbl 1366.17014); J. Am. Math. Soc. 31, No. 2, 349–426 (2018; Zbl 1460.13039); M. Kashiwara et al., Adv.
Math. 328, 959–1009 (2018; Zbl 1437.17005); M. Kashiwara and E. Park, J. Eur. Math. Soc. (JEMS)
20, No. 5, 1161–1193 (2018; Zbl 1475.16024)]. In the representation theory of quantum affine algebras,
R-matrices already occupy a significant position. The generalized Schur-Weyl duality functor relates the
R-matrices in quiver Hecke algebras and the ones in quantum affine algebras in a natural way, and they
enjoy very similar properties in their own categories [V. Chari and A. Pressley, A guide to quantum
groups. Cambridge: Cambridge University Press (1994; Zbl 0839.17009); P. I. Etingof and A. A. Moura,
Represent. Theory 7, 346–373 (2003; Zbl 1066.17005); M. Kashiwara, Duke Math. J. 112, No. 1, 117–195
(2002; Zbl 1033.17017); S.-J. Kang et al., Invent. Math. 211, No. 2, 591–685 (2018; Zbl 1407.81108); S.-J.
Kang et al., Invent. Math. 216, No. 2, 597–599 (2019; Zbl 1447.81140); M. Kashiwara et al., Compos.
Math. 156, No. 5, 1039–1077 (2020; Zbl 1497.17020), M. Kashiwara et al., Invent. Math. 236, No. 2,
837–924 (2024; Zbl 07828037)].
This paper establishes the theory of affinization and R-matrices in the language of pro-objects, and as an
application, constructs reflection functors over the localizations of quiver Hecke algebras of an arbitrary
finite type. The main results of the paper goes as follows.
The first main result is to study the notion of affinization and R-matrices in the language of pro-objects. The authors
define affinizations and R-matrices in the categories with certain conditions, investigating their
properties. Key properties appearing in quiver Hecke algebras and quantum affine algebras are re-
discovered in a purely categorical setting. The authors next introduce a duality datum at the category
level, constructing a generalized Schur-Weyl duality in the category setting after [M. Kashiwara et
al., Invent. Math. 236, No. 2, 837–924 (2024; Zbl 07828037)].
The second main result is to apply the generalized Schur-Weyl duality to the localized category C̃∗si,w0 of a quiver Hecke
algebra of arbitrary finite type. As a result, for any i ∈ I, the authors obtain an equivalence of
monoidal categories
Si : C̃si,w0
∼→ C̃∗si,w0
which categorifies the braid group action [G. Lusztig, Introduction to quantum groups. Boston, MA:
Birkhäuser (1993; Zbl 0788.17010), Chapter 37] and the Saito reflection σi [Y. Saito, Publ. Res.
Inst. Math. Sci. 30, No. 2, 209–232 (1994; Zbl 0812.17013)].
Reviewer: Hirokazu Nishimura (Tsukuba)
MSC:
18M05 Monoidal categories, symmetric monoidal categories
16D90 Module categories in associative algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations
Keywords:
affinization; localization; reflection; R-matrices; quiver Hecke algebra
Full Text: DOI arXiv
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 1
References:
[1] Chari, V.; Pressley, A., A Guide to Quantum Groups, 1994, Cambridge University Press: Cambridge University Press Cam-
bridge · Zbl 0839.17009
[2] Chriss, N.; Ginzburg, V., Representation Theory and Complex Geometry, 1997, Birkhäuser Boston, Inc.: Birkhäuser Boston,
Inc. Boston, MA · Zbl 0879.22001
[3] Etingof, P.; Gelaki, S.; Nikshych, D.; Ostrik, V., Tensor Categories, Mathematical Surveys and Monographs, vol. 205, 2015,
American Mathematical Society: American Mathematical Society Providence, RI, xvi+343 pp. · Zbl 1365.18001
[4] Etingof, P.; Moura, A. A., Elliptic central characters and blocks of finite dimensional representations of quantum affine
algebras, Represent. Theory, 7, 346-373, 2003 · Zbl 1066.17005
[5] Kashiwara, M., On level zero representations of quantum affine algebras, Duke Math. J., 112, 117-175, 2002 · Zbl 1033.17017
[6] Kang, S.-J.; Kashiwara, M.; Kim, M.; Oh, S-j., Simplicity of heads and socles of tensor products, Compos. Math., 151, 2,
377-396, 2015 · Zbl 1366.17014
[7] Kang, S.-J.; Kashiwara, M.; Kim, M., Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras, Invent.
Math., 211, 591-685, 2018 · Zbl 1407.81108
[8] Kang, S.-J.; Kashiwara, M.; Kim, M., Monoidal categorification of cluster algebras, J. Am. Math. Soc., 31, 2, 349-426, 2018 ·
Zbl 1460.13039
[9] Kashiwara, M.; Kim, M.; Oh, S-j.; Park, E., Monoidal categories associated with strata of flag manifolds, Adv. Math., 328,
959-1009, 2018 · Zbl 1437.17005
[10] Kashiwara, M.; Kim, M.; Oh, S-j.; Park, E., Monoidal categorification and quantum affine algebras, Compos. Math., 156, 5,
1039-1077, 2020 · Zbl 1497.17020
[11] Kashiwara, M.; Kim, M.; Oh, S-j.; Park, E., Localizations for quiver Hecke algebras, Pure Appl. Math. Q., 17, 4, 1465-1548,
2021 · Zbl 1495.18020
[12] Kashiwara, M.; Kim, M.; Oh, S-j.; Park, E., Localizations for quiver Hecke algebras II, Proc. Lond. Math. Soc. (4), 127,
1134-1184, 2023 · Zbl 07785233
[13] Kashiwara, M.; Park, E., Affinizations and R-matrices for quiver Hecke algebras, J. Eur. Math. Soc., 20, 1161-1193, 2018 ·
Zbl 1475.16024
[14] Kashiwara, M.; Schapira, P., Categories and Sheaves, Grundlehren der Mathematischen Wissenschaften, vol. 332, 2006,
Springer-Verlag: Springer-Verlag Berlin · Zbl 1118.18001
[15] Kato, S., Poincaré-Birkhoff-Witt bases and Khovanov-Lauda-Rouquier algebras, Duke Math. J., 163, 3, 619-663, 2014 · Zbl
1292.17012
[16] Kato, S., On the monoidality of Saito reflection functors, Int. Math. Res. Not., 22, 8600-8623, 2020 · Zbl 1479.16010
[17] Khovanov, M.; Lauda, A., A diagrammatic approach to categorification of quantum groups I, Represent. Theory, 13, 309-347,
2009 · Zbl 1188.81117
[18] Khovanov, M.; Lauda, A., A diagrammatic approach to categorification of quantum groups II, Trans. Am. Math. Soc., 363,
2685-2700, 2011 · Zbl 1214.81113
[19] Lauda, A.; Vazirani, M., Crystals from categorified quantum groups, Adv. Math., 228, 2, 803-861, 2011 · Zbl 1246.17017
[20] Lusztig, G., Introduction to Quantum Groups, Progr. Math., vol. 110, 1993, Birkhäuser · Zbl 0788.17010
[21] McNamara, P. J., Finite dimensional representations of Khovanov-Lauda-Rouquier algebras I: finite type, J. Reine Angew.
Math., 707, 103-124, 2015 · Zbl 1378.17018
[22] McNamara, P. J., Monoidality of Kato’s reflection functors
[23] Rouquier, R., 2-Kac-Moody algebras
[24] Saito, Y., PBW basis of quantized universal enveloping algebras, Publ. Res. Inst. Math. Sci., 30, 2, 209-232, 1994 · Zbl
0812.17013
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1696, 2016 · Zbl 1425.17022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically
matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original
paper as accurately as possible without claiming the completeness or perfect precision of the matching.
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 2


English

a review of Affinizations R-matrices and reflection functors by Kashiwara Masaki; Kim Myungho; Oh Se-jin; Park Euiyong

Moriya, Syunji
Models for knot spaces and Atiyah duality. (English)
  Zbl 07827840
Algebr. Geom. Topol. 24, No. 1, 183-250 (2024)
D. P. Sinha [J. Am. Math. Soc. 19, No. 2, 461–486 (2006; Zbl 1112.57004); Am. J. Math. 131, No. 4, 945–
980 (2009; Zbl 1184.57023)] constructed cosimplicial models of spaces of knots in a manifold of dimension
≥ 4, based on Goodwillie-Weise embedding calculus [T. G. Goodwillie and J. R. Klein, J. Topol. 8, No.
3, 651–674 (2015; Zbl 1329.57029); T. G. Goodwillie and M. Weiss, Geom. Topol. 3, 103–118 (1999; Zbl
0927.57028); M. Weiss, Geom. Topol. 3, 67–101 (1999; Zbl 0927.57027); Geom. Topol. 15, No. 1, 407–409
(2011; Zbl 1208.57013)]. The model was crucially exploited in the affirmative solution to V. A. Vassiliev’s
conjecture [Transl. Math. Monogr. 185, 155–182 (1998; Zbl 0929.57004)] for the space of long knots in
Rd (d ≥ 4) for rational coefficients in [P. Lambrechts et al., Geom. Topol. 14, No. 4, 2151–2187 (2010;
Zbl 1222.57020)]. This paper investigates a version of Sinha’s model in stable categories. M denotes a
connected closed smooth manidold of dimension d.
The synopsis of the paper goes as follows.
§2 introduces basic notions, defining of Sinha’s cosimplicial model and showing that its homotopy
limit is equivalent to the space Emb
(
S1, M
)
of smooth embeddings S1 → M rigged with the C∞-
topology. The notions of a (co)module and Hochschild complex of a comodule over the associahedral
operad are delineated.
§3 is the technical heart of the paper, introduccing a version of Cohen’s model of Thom spectra (called
the Sinha’s cosimplicial model and denoted by C· (M)) and using it to construct the comodule TM
whose nth object is a natural model of the Thom spectrum
Σ−nKTh (υn) /Th (υn |F Dn)
where
– Σ denotes the suspension equivalence and Th (−) denotes the associated Thom space,
– FDn is the preimage of the fat diagonal by (the product of) the projections SMn → Mn, and
– υn |F Dn denotes the restriction of the base to FDn.
§4 establishes Theorem 1.1 claiming a dual equivalence between the configuration spaces and quotients
by a fat diagonal
(CM )∨ ≃ TM
where (CM )∨ is a comodule whose nth object is the Spanier-Whitehead dual [E. H. Spanier and J. H.
C. Whitehead, Proc. Natl. Acad. Sci. USA 39, 655–660 (1953; Zbl 0051.14001); Mathematika 2, 56–
80 (1955; Zbl 0064.17202); Ann. Math. (2) 67, 203–238 (1958; Zbl 0092.15701)] of the configuration
space of n points with a tangent vector in M .
§5 defines a chain functor for symmetric spectra and constructs the spectral sequence filtering Hochschild
complex of the chains of a resolution of the comodule TM . It is established that the E1-page of the
Čech spectral sequence is quasi-isomorphic to the total complex of a simplicial differential bigraded
algebra. The convergence of the Čech spectral sequence is demonstrated.
§6 computes the cohomology ring H∗ (DG) and maps between them, giving a description of the sim-
plicial algebra in terms of the cohomology ring H∗ (M) under some assumptions. The computation
is standard after Serre spectral sequences.
§7 computes examples, establishing under some assumptions that the inclusion
iM : Emb
(
S1, M
)
→ Imm
(
S1, M
)
with Imm
(
S1, M
)
the space of smooth immersions S1 → M with the C∞-topology induces an
isomorphism on π1.
Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
© 2024 FIZ Karlsruhe GmbH Page 1
§8 resolves Sinha’s cosimplicial model, considered as a resolution of Emb
(
S1, M
)
into simpler spaces,
further simpler pieces in the category of chain complexes.
Reviewer: Hirokazu Nishimura (Tsukuba)
MSC:
18M75 Topological and simplicial operads
55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)
55T99 Spectral sequences in algebraic topology
57R40 Embeddings in differential topology
18N40 Homotopical algebra, Quillen model categories, derivators
Keywords:
embedding calculus; operad; knot space
Full Text: DOI arXiv
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a review of Models for knot spaces and Atiyah duality by Moriya Syunji

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