Exploring Information Geometry
close menu
Bookswagon
search
My Account
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science books > Mathematics > Geometry > Differential and Riemannian geometry > Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)
Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)

Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

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.

 



Table of Contents:

Introduction.- Foundations of General Topology.- Topological and Modeled Manifolds.- Differentiability and Gateaux Derivatives.- Fiber Bundles.- Connections, Parallel Transport, and Sheafs.- Probability Theory, Measure Theory, and Statistics.- Categorical Structures in Probability and Measure Theory.- Categorical and Geometric Structures in Statistical Manifold Theory.- Frobenius Manifolds.- Unveiling the Hidden Geometry of Statistical Manifolds.- Statistical Frobenius Manifolds and Learning.



About the Author :
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.


Best Sellers


Product Details
  • ISBN-13: 9783032230539
  • Publisher: Springer Nature Switzerland AG
  • Publisher Imprint: Birkhauser
  • Height: 240 mm
  • No of Pages: 228
  • Returnable: N
  • Returnable: N
  • Returnable: N
  • Returnable: N
  • Series Title: Frontiers in Mathematics
  • Width: 168 mm
  • ISBN-10: 3032230535
  • Publisher Date: 10 Aug 2026
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Returnable: N
  • Returnable: N
  • Returnable: N
  • Sub Title: Recent Advances and Connections to Topological Field Theory


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)
Springer Nature Switzerland AG -
Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Exploring Information Geometry: Recent Advances and Connections to Topological Field Theory(Frontiers in Mathematics)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!