Low Dimensional Topology and Number Theory: Fukuoka, Japan, March 15-18, 2022. in Memory of Professor Toshie Takata
暫譯: 低維拓撲與數論：2022年3月15日至18日，福岡，日本，紀念高田敏惠教授
Morishita, Masanori, Nakamura, Hiroaki, Ueki, Jun
- 出版商: Springer
- 出版日期: 2025-03-02
- 售價: $7,960
- 貴賓價: 9.5 折 $7,562
- 語言: 英文
- 頁數: 380
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 981973777X
- ISBN-13: 9789819737772
海外代購書籍(需單獨結帳)
商品描述
This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory XIII" at Kyushu University in 2022. It is also dedicated to the memory of Professor Toshie Takata, who has been a main figure of the session chairs for the series of annual workshops since 2009.
The activity was aimed at understanding and deepening recent developments of lively and fruitful interactions between low-dimensional topology and number theory over the past decades.
In this volume of proceedings, the reader will find research papers as well as survey articles, including open problems, at the interface between classical and quantum topology, and algebraic and analytic number theory, written by leading experts and active researchers in the respective fields.
Topics include, among others, the strong slope conjecture; Kashiwara-Vergne Lie algebra; braids and fibered double branched covers of 3-manifolds; Temperley-Lieb-Jones category andconformal blocks; WRT invariants and false theta functions; the colored Jones polynomial of the figure-eight knot; potential functions and A-polynomials; l-adic Galois polylogarithms; Dijkgraaf-Witten invariants in Bloch groups; analogies between knots and primes in arithmetic topology; normalized Jones polynomials for rational links; Iwasawa main conjecture; Weber's class number problem.
The book provides a valuable resource for researchers and graduate students interested in topics related to both low-dimensional topology and number theory.
商品描述(中文翻譯)
這本書是2022年於九州大學舉辦的「低維拓撲與數論第十三屆研討會」期間形成的研究計畫的成果。它也獻給高田敏恵教授的記憶，自2009年以來，她一直是這系列年度研討會的主要會議主席。
這項活動旨在理解和深化過去幾十年來低維拓撲與數論之間生動而富有成效的互動的最新發展。
在這本會議論文集中，讀者將會找到研究論文以及調查文章，包括經典與量子拓撲、代數與解析數論之間的開放問題，這些文章由各自領域的領先專家和活躍研究人員撰寫。
主題包括但不限於：強斜率猜想；Kashiwara-Vergne李代數；編織與三維流形的纏繞雙分支覆蓋；Temperley-Lieb-Jones類別與共形區塊；WRT不變量與虛假θ函數；八字結的彩色Jones多項式；潛在函數與A-多項式；l-進Galois多重對數；Dijkgraaf-Witten不變量在Bloch群中的應用；結與算術拓撲中的質數之間的類比；有理鏈的標準化Jones多項式；岩澤主猜想；韋伯的類數問題。
這本書為對低維拓撲和數論相關主題感興趣的研究人員和研究生提供了寶貴的資源。
作者簡介
Masanori Morishita is professor of mathematics at Kyushu University, Fukuoka Japan.
He is one of the primary pioneers who established "Arithmetic Topology"-- a new branch of mathematics which is focused upon the analogy between knot theory and number theory. He authored the first systematic treatment of the subject in the book "Knots and Primes" (Universitext) published from Springer in 2012. Since 2009, he has organized a series of international annual meetings "Low dimensional topology and number theory" that enhances the community of mathematicians in the world who contribute to the active frontiers of the promising area interacting with topology and number theory.
Hiroaki Nakamura is professor of mathematics at Osaka University, Osaka Japan.
He is a world-leading figure in anabelian geometry and Galois-Teichmüller theory in arithmetic algebraic geometry. He is known as the first person who made a break-through on Grothendieck's conjecture in anabelian geometry by solving it in the case of genus 0, and he was awarded Autumn Prize of the Mathematical Society of Japan.
His outstanding contributions to mathematics are cross over number theory, algebraic geometry and topology. He is also an organizer of the international annual meetings "Low dimensional topology and number theory" and is enrolled in the scientific committee of "LPP-RIMS Arithmetic and Homotopic Galois Theory"-- CNRS France-Japan International Research Network.
Jun Ueki is a senior lecturer of mathematics at Ochanomizu University, Tokyo Japan.
He is an active researcher, who is leading the young generation, in arithmetic topology. He made a pioneering contribution on a topological idelic theory for 3-manifolds, and his notable works range over arithmetic topology of branched covers of 3-manifolds in connection with Iwasawa theory, the profinite rigidity of twisted Alexander invariants, and modular knots.He is also an organizer of the international annual meetings "Low dimensional topology and number theory".
作者簡介(中文翻譯)
森下雅則（Masanori Morishita）是日本福岡九州大學的數學教授。他是建立「算術拓撲」（Arithmetic Topology）的主要先驅之一，這是一個專注於結理論與數論之間類比的新數學分支。他在2012年出版的書籍《Knots and Primes》（Universitext）中，對該主題進行了首次系統性的處理。自2009年以來，他組織了一系列國際年度會議「低維拓撲與數論」（Low dimensional topology and number theory），以促進全球數學家社群，這些數學家對於拓撲學與數論交互作用的有前景領域做出貢獻。
中村宏明（Hiroaki Nakamura）是日本大阪大學的數學教授。他是算術代數幾何中的無可比擬幾何（anabelian geometry）和伽羅瓦-泰希穆勒理論（Galois-Teichmüller theory）的世界領先人物。他被認為是第一位在無可比擬幾何中突破格羅滕迪克猜想（Grothendieck's conjecture）的人，並在 genus 0 的情況下解決了該問題，因此獲得了日本數學會的秋季獎（Autumn Prize）。
他對數學的卓越貢獻跨越了數論、代數幾何和拓撲學。他也是國際年度會議「低維拓撲與數論」的組織者，並參與「LPP-RIMS 算術與同倫伽羅瓦理論」（LPP-RIMS Arithmetic and Homotopic Galois Theory）科學委員會，該委員會是法國國家科學研究中心（CNRS）與日本的國際研究網絡。
上木純（Jun Ueki）是日本東京的御茶水女子大學的高級講師。他是一位活躍的研究者，領導著年輕一代的算術拓撲研究。他在三維流形的拓撲理想理論（topological idelic theory）方面做出了開創性的貢獻，他的顯著工作涵蓋了與岩澤理論（Iwasawa theory）相關的三維流形的分支覆蓋的算術拓撲、扭曲亞歷山大不變量的有限剛性（profinite rigidity）以及模數結（modular knots）。
他也是國際年度會議「低維拓撲與數論」的組織者。
