Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory (Paperback)
暫譯: 探索資訊幾何：近期進展與拓撲場論的關聯（平裝本）

Combe, Noémie C., Combe, Philippe G., Nencka, Hanna K.

Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory (Paperback)
  • 出版商: Birkhauser Boston
  • 出版日期: 2026-07-26
  • 售價: $2,710
  • 貴賓價: 9.5 折 $2,574
  • 語言: 英文
  • 頁數: 271
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032230535
  • ISBN-13: 9783032230539
  • 相關分類: 機率統計學 Probability-and-statistics

    • 海外代購書籍(需單獨結帳)

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商品描述

This book offers a clear and accessible pathway into information geometry for advanced undergraduate and graduate students. Readers will be guided from the fundamentals of topology and differentiable manifolds to the more advanced concepts of probability geometry and Frobenius manifolds in an intuitive manner, allowing them to build their knowledge gradually. Divided into three main parts, the first provides a concise introduction to differential topology and geometry, emphasizing the role of smooth manifolds, connections, and curvature in the formulation of geometric structures. Part II is then devoted to probability, measures, and statistics, where the notion of a probability space is refined into a geometric object, thus paving the way for a deeper mathematical understanding of statistical models. Finally, the third part introduces Frobenius manifolds, revealing their surprising connection to exponential families of probability distributions and, more broadly, their role in the geometry of information. Throughout all the chapters, there are exercises to test understanding, as well as solutions to some of the more challenging problems to aid learning.

 

 

商品描述(中文翻譯)

本書為高年級大學生與研究生提供一條清晰且易於理解的資訊幾何（information geometry）入門途徑。讀者將以直觀的方式，從拓撲學與可微流形（differentiable manifolds）的基礎概念，逐步學習機率幾何（probability geometry）與 Frobenius 流形等進階主題，循序建立相關知識。

全書分為三個主要部分。第一部分簡明介紹微分拓撲與微分幾何，著重說明光滑流形（smooth manifolds）、聯絡（connections）與曲率（curvature）在幾何結構表述中所扮演的角色。第二部分探討機率、測度與統計，將機率空間的概念深化為一種幾何物件，為更深入理解統計模型奠定數學基礎。最後，第三部分介紹 Frobenius 流形，揭示其與機率分布的指數族（exponential families）之間令人意外的關聯，以及更廣泛而言，它們在資訊幾何中的作用。

全書各章皆附有練習題，以檢驗讀者的理解程度；此外，也提供部分較具挑戰性問題的解答，協助讀者學習。

作者簡介

Noémie Combe is a mathematician and research professor at the Léonard de Vinci University Pole. She has secured several prestigious research grants, serving as principal investigator and group leader of the renowned Polonez Bis 3 programme--funded by Horizon 2020--at the University of Warsaw. Prior to this, she led a Minerva Group at the Max Planck Society for five years, where her research received significant recognition and sustained support. She earned her degrees from the University of Geneva, and completed her PhD at the University of Aix--Marseille and Sorbonne University (Paris 6).

 

Philippe Combe is an emeritus professor of Mathematical Physics at the University of Aix-Marseille, as well as a long‐standing member of the Centre for Theoretical Physics (CPT). Over a distinguished career spanning more than four decades, he has made foundational contributions to functional analysis, group theory, operator theory, geometry, statistics, and stochastic process. His work is characterized by high‐impact collaborations across Europe and beyond. In addition to his research, Philippe Combe has provided key leadership in the scientific community.

 

Hanna Nencka is a distinguished invited researcher in the Polonez Bis 3-sponsored Research Group at the University of Warsaw. She has held tenured professorships at Columbia University (USA), the Polish Academy of Science, and the University of Madeira (Portugal). Her prolific scholarship includes over one hundred peer-reviewed publications in leading journals. Her pioneering contributions to mathematical physics have earned her international recognition and multiple research awards, namely from the Polish Academy of Sciences for outstanding work.

 

作者簡介(中文翻譯)

Noémie Combe 是一位數學家，也是 Léonard de Vinci University Pole 的研究教授。她曾獲得多項享有盛譽的研究獎助，擔任首席研究員與研究團隊領導人，並在 University of Warsaw 領導由 Horizon 2020 資助、享有盛名的 Polonez Bis 3 計畫。在此之前，她曾於 Max Planck Society 領導 Minerva Group 五年，其研究成果獲得高度肯定與持續支持。她在 University of Geneva 取得學位，並於 University of Aix-Marseille 與 Sorbonne University（Paris 6）完成博士學位。

Philippe Combe 是 University of Aix-Marseille 的數理物理學榮譽教授，也是 Centre for Theoretical Physics（CPT）的長期成員。在超過四十年的傑出學術生涯中，他對泛函分析、群論、算子理論、幾何學、統計學與隨機過程作出了奠基性貢獻。他的研究以跨越歐洲及其他地區、具有高度影響力的合作為特色。除了研究工作之外，Philippe Combe 也曾在科學社群中擔任重要的領導角色。

Hanna Nencka 是 University of Warsaw 中由 Polonez Bis 3 資助之研究團隊的傑出客座研究員。她曾於 Columbia University（美國）、Polish Academy of Science 及 University of Madeira（葡萄牙）擔任具終身職資格的教授。她學術成果豐碩，在頂尖期刊發表了超過一百篇經同儕審查的論文。她在數理物理學領域的先驅性貢獻，為她贏得國際聲譽與多項研究獎項，其中包括 Polish Academy of Sciences 頒發的傑出研究獎。

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