Spectral Networks: Bridging Higher-Rank Teichmüller Theory and Bps States
暫譯: 光譜網絡：連結高階 Teichmüller 理論與 BPS 狀態

Kineider, Clarence, Kydonakis, Georgios, Rogozinnikov, Eugen

Spectral Networks: Bridging Higher-Rank Teichmüller Theory and Bps States
  • 出版商: Springer
  • 出版日期: 2026-04-26
  • 售價: $3,870
  • 貴賓價: 9.5 折 $3,676
  • 語言: 英文
  • 頁數: 524
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032092183
  • ISBN-13: 9783032092182
  • 相關分類: 數學

    • 海外代購書籍(需單獨結帳)

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商品描述

This open access book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the foundational background needed to approach the frontiers of this rapidly evolving field, treating geometric and physical aspects in parallel. After surveying fundamental topics in algebra and geometry, a detailed introduction to higher-rank Teichmüller theory is developed, including Fock-Goncharov theory for Hitchin representations, maximal representations and the more recent notion of Θ-positivity.

Spectral networks are subsequently introduced, emphasizing their utility in the study of character varieties via the abelianization and non-abelianization maps they define. In parallel, key aspects of four-dimensional gauge dynamics with eight supercharges are explored, including electric-magnetic duality, Seiberg-Witten theory, and class S theories. The role of spectral networks as a framework for determining and analyzing BPS spectra in class S theories is then examined. The final chapter outlines recent applications of spectral networks across a range of contemporary research areas.

This volume is intended for researchers and advanced students in either mathematics or physics who wish to enter the field.

商品描述(中文翻譯)

這本開放存取的書籍從統一的視角提供了對光譜網絡的全面介紹，將幾何學與超對稱規範理論的物理學橋接起來。它提供了進入這個快速發展領域所需的基礎背景，並平行處理幾何和物理方面的內容。在概述代數和幾何的基本主題後，詳細介紹了高階 Teichmüller 理論，包括針對 Hitchin 表示的 Fock-Goncharov 理論、最大表示以及最近提出的 Θ-正性概念。

隨後介紹了光譜網絡，強調它們在通過所定義的阿貝爾化和非阿貝爾化映射研究特徵變種中的實用性。同時，探討了具有八個超電荷的四維規範動力學的關鍵方面，包括電-磁對偶性、Seiberg-Witten 理論和類 S 理論。然後檢視了光譜網絡作為確定和分析類 S 理論中 BPS 光譜的框架的角色。最後一章概述了光譜網絡在當代研究領域中的最新應用。

本書旨在為希望進入該領域的數學或物理學研究者和高級學生提供參考。

作者簡介

Clarence Kineider studied mathematics at the École Normale Supérieure de Rennes and the University of Strasbourg between 2016 and 2019. He completed his Ph.D. at the University of Strasbourg, where his research focused on higher Teichmüller spaces, Fock-Goncharov coordinates, and spectral networks. Since 2024, he has been a postdoctoral fellow at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

Georgios Kydonakis studied Mathematics (B.Sc.) at the University of Athens in Greece and obtained his Ph.D. degree from the University of Illinois at Urbana-Champaign in the USA. He has held postdoctoral positions in Strasbourg, Bonn, and Heidelberg as an Alexander von Humboldt fellow. Since 2023, he has been an Assistant Professor at the University of Patras in Greece. His research interests lie on the crossroad between complex geometry and mathematical physics.

Eugen Rogozinnikov studied mathematics at the University of Heidelberg, where he completed his master's degree in 2016 and received his Ph.D. in mathematics in 2020. After that, he held a postdoctoral position at the Université de Strasbourg. In 2023-2024, he was a DAAD fellow at the University of Notre Dame (USA). He later worked at the Max Planck Institute for Mathematics in the Sciences in Leipzig and is currently a research fellow at the Korea Institute for Advanced Study (KIAS) in Seoul. His research interests include differential geometry, geometric topology, and higher Teichmüller theory.

Valdo Tatitscheff studied mathematics and physics at the École normale supérieure de la rue d'Ulm in Paris from 2014 to 2018, and earned a Ph.D. in mathematics from the University of Strasbourg and the Institut de Recherche Mathématique Avancée (IRMA) in 2022. Currently a Postdoctoral Fellow at the Institute for Mathematics at Heidelberg University, Tatitscheff's main research interests lie at the interface of geometry and gauge theories.

Alexander Thomas studied mathematics at the École Normale Supérieure de Lyon from 2013 to 2017 and completed his Ph.D. at the University of Strasbourg in 2020. He held postdoctoral positions at the Max Planck Institute for Mathematics in Bonn (2020-2022) and at the University of Heidelberg (2022-2024). Since 2024, he has been a Maître de Conférences (Associate Professor) at Université Claude Bernard Lyon 1. His research focuses primarily on gauge theory and quantum algebra.

作者簡介(中文翻譯)

克拉倫斯·基奈德於2016年至2019年間在法國雷恩高等師範學校（École Normale Supérieure de Rennes）和斯特拉斯堡大學（University of Strasbourg）學習數學。他在斯特拉斯堡大學完成了博士學位，研究重點為高階Teichmüller空間、Fock-Goncharov座標和光譜網絡。自2024年以來，他在萊比錫的馬克斯·普朗克科學數學研究所擔任博士後研究員。 喬治奧斯·基多納基斯在希臘雅典大學獲得數學學士學位（B.Sc.），並在美國伊利諾伊大學香檳分校獲得博士學位。他曾在斯特拉斯堡、波恩和海德堡擔任亞歷山大·馮·洪堡獎學金的博士後研究員。自2023年以來，他在希臘帕特雷大學擔任助理教授。他的研究興趣位於複幾何和數學物理的交叉點。 尤金·羅戈津尼科夫在海德堡大學學習數學，於2016年獲得碩士學位，並於2020年獲得數學博士學位。之後，他在斯特拉斯堡大學擔任博士後研究員。在2023至2024年間，他是美國聖母大學的DAAD獎學金獲得者。之後，他在萊比錫的馬克斯·普朗克科學數學研究所工作，目前是首爾高等研究院（Korea Institute for Advanced Study, KIAS）的研究員。他的研究興趣包括微分幾何、幾何拓撲和高階Teichmüller理論。 瓦爾多·塔提切夫於2014年至2018年間在巴黎的烏爾姆街高等師範學校（École normale supérieure de la rue d'Ulm）學習數學和物理，並於2022年從斯特拉斯堡大學和數學高級研究所（Institut de Recherche Mathématique Avancée, IRMA）獲得數學博士學位。目前，他是海德堡大學數學研究所的博士後研究員，塔提切夫的主要研究興趣位於幾何和規範理論的交界處。 亞歷山大·托馬斯於2013年至2017年間在里昂高等師範學校（École Normale Supérieure de Lyon）學習數學，並於2020年在斯特拉斯堡大學完成博士學位。他曾在波恩的馬克斯·普朗克數學研究所（2020-2022）和海德堡大學（2022-2024）擔任博士後研究員。自2024年以來，他在克勞德·伯納德·里昂第一大學（Université Claude Bernard Lyon 1）擔任副教授（Maître de Conférences）。他的研究主要集中在規範理論和量子代數上。

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