Low Dimensional Topology and Number Theory: Fukuoka, Japan, March 15-18, 2022. in Memory of Professor Toshie Takata
Morishita, Masanori, Nakamura, Hiroaki, Ueki, Jun
- 出版商: Springer
- 出版日期: 2025-02-12
- 售價: $7,700
- 貴賓價: 9.5 折 $7,315
- 語言: 英文
- 頁數: 380
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 981973777X
- ISBN-13: 9789819737772
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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年在九州大學舉辦的「低維拓撲與數論第十三屆」研討會期間形成的研究計畫的結果。同時，這本書也是獻給教授高田敏江的紀念，她自2009年以來一直是這一系列年度研討會的主要主席。
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活躍且豐富的互動的最新發展。
在這本論文集中，讀者將找到由各領域的領先專家和活躍研究者撰寫的研究論文和綜述文章，包括開放問題，這些文章介於傳統和量子拓撲、代數和分析數論之間的交界面。
主題包括但不限於強斜率猜想、柏原-維爾涅李代數、辮子和三維流形的纖維雙分支覆蓋、Temperley-Lieb-Jones類別和共形區塊、WRT不變量和虛假θ函數、八字結的彩色Jones多項式、潛在函數和A-多項式、l-進Galois多對數、Bloch群中的Dijkgraaf-Witten不變量、算術拓撲中結和質數之間的類比、有理鏈結的規範化Jones多項式、岩澤主猜想、韋伯的類數問題。
這本書對於對低維拓撲和數論相關主題感興趣的研究人員和研究生來說是一個寶貴的資源。
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)
森下正則是日本福岡九州大學的數學教授。
他是建立「算術拓撲學」的主要先驅之一，這是一個專注於結繩理論和數論之間類比的新數學分支。他在2012年由Springer出版的《結繩與質數》（Universitext）一書中，撰寫了對這一主題的首次系統性研究。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」，促進了世界上那些致力於與拓撲學和數論相互作用的前沿領域的數學家社群。
中村宏明是日本大阪大學的數學教授。
他是算術代數幾何學中「anabelian幾何學」和「Galois-Teichmüller理論」的世界領先人物。他以解決了Grothendieck在anabelian幾何學中的猜想（在屬於0層的情況下）而聞名，並獲得了日本數學學會的秋季獎。
他在數論、代數幾何學和拓撲學方面做出了傑出貢獻。他還是國際年度會議「低維拓撲與數論」的組織者，並且是「LPP-RIMS算術和同調Galois理論」的科學委員會成員，該組織是法國國家科學研究中心和日本的國際研究網絡。
植木淳是日本東京御茶水女子大學的高級講師。
他是活躍的研究者，引領著年輕一代在算術拓撲學領域的發展。他對於3維流形的拓撲理想理論做出了開創性的貢獻，他的重要工作涉及到與岩澤理論相關的3維流形的分支覆蓋的算術拓撲學、扭曲亞歷山大不變量的有限完備性和模節點。
他還是國際年度會議「低維拓撲與數論」的組織者。
