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Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces: Based on Lectures Given at a Conference on Integrable Systems Organized by N.M.J. Woodhouse and Held at the Mathematical Institute, University of Oxford, in September 1997

Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics, 4)

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Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces: Based on Lectures Given at a Conference on Integrable Systems Organized by N.M.J. Woodhouse and Held at the Mathematical Institute, University of Oxford, in September 1997

Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces (Oxford Graduate Texts in Mathematics, 4)

4.85 92,696 ratings · 9,599 reviews
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Overview: This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles. Graeme Segal takes the Kortewegde Vries and nonlinear SchrAdinger equations as central examples, and explores themathematical structures underlying the inverse scattering transform. He explains the roles of loop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and the self-dual Yang-Mills equations, and describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.

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Pages 147
Publisher Not Avail
Published May 13, 1999
ISBN 23022734
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N.J. Hitchin
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N.J. Hitchin writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. N.J. Hitchin lives with their spouse and a very vocal rescue cat.

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Sharon Wilson
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Mark Lopez
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Donna Brown
Donna Brown March 16, 2024
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William Parker April 12, 2024
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Melissa Ramirez January 14, 2024
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Barbara Gonzalez May 19, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Jennifer Hall June 09, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
George Martinez
George Martinez April 28, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Sharon Nelson
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Robert Roberts
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
John Roberts
John Roberts November 16, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Eric Lopez
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Nicholas Cruz
Nicholas Cruz January 24, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Cynthia Hill
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Donna Ramirez May 19, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Jennifer Martinez
Jennifer Martinez February 14, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Mark Hernandez April 25, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Rebecca Hall
Rebecca Hall January 18, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
James Jones
James Jones September 25, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Jessica Green
Jessica Green June 16, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Betty Gomez
Betty Gomez November 30, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Linda Lee
Linda Lee June 06, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Kevin Nelson
Kevin Nelson October 11, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Richard Rivera
Richard Rivera May 06, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Sandra Jackson
Sandra Jackson October 27, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Charles White
Charles White March 29, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Matthew Edwards
Matthew Edwards September 04, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Susan Brown
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Ryan Young
Ryan Young October 03, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Kenneth Scott
Kenneth Scott January 05, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Donald Lewis
Donald Lewis October 01, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Patricia  Parker
Patricia Parker October 26, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Edward Johnson
Edward Johnson May 26, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Sarah Walker
Sarah Walker December 22, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
David Taylor
David Taylor October 16, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Anthony Taylor
Anthony Taylor February 22, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Mark Allen
Mark Allen February 26, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Carol Davis April 07, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
John White
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Joshua Flores
Joshua Flores August 08, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Stephanie Flores
Stephanie Flores March 05, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Cynthia Reyes
Cynthia Reyes May 21, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Sharon Jackson
Sharon Jackson May 15, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Donna Turner
Donna Turner December 16, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Betty Gomez
Betty Gomez October 22, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
John Allen
John Allen January 03, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Anthony Taylor
Anthony Taylor December 11, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
George Johnson
George Johnson January 05, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Jacob Hall
Jacob Hall April 10, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Laura Thomas
Laura Thomas October 31, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Carol Reyes June 24, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Kevin Lee
Kevin Lee November 16, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Linda Baker
Linda Baker July 13, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Kevin White
Kevin White October 23, 2024
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Christopher Walker
Christopher Walker October 05, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Cynthia Lee
Cynthia Lee September 28, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Cynthia Hill
Cynthia Hill March 16, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Barbara Turner
Barbara Turner February 07, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Rebecca Green
Rebecca Green January 05, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Barbara Jackson
Barbara Jackson April 17, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Nancy  Parker
Nancy Parker October 17, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
James  Davis
James Davis September 07, 2024
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Kenneth Wright
Kenneth Wright December 26, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Sandra Martin
Sandra Martin August 24, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Joseph Nguyen
Joseph Nguyen July 02, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Eric Martinez
Eric Martinez March 25, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Dorothy Rodriguez
Dorothy Rodriguez April 29, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Kimberly Taylor
Kimberly Taylor September 14, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Barbara Gonzalez
Barbara Gonzalez August 02, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Jacob Reyes
Jacob Reyes November 11, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Edward Johnson
Edward Johnson March 17, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Melissa Edwards
Melissa Edwards August 09, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Matthew Hernandez
Matthew Hernandez December 05, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Donald Lewis
Donald Lewis February 10, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Ryan Lopez
Ryan Lopez January 06, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Robert Thompson
Robert Thompson June 02, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Steven Cruz
Steven Cruz March 31, 2025
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Eric Reyes
Eric Reyes January 10, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Nicholas Collins
Nicholas Collins October 18, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Mark Wright
Mark Wright January 05, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Eric Gomez
Eric Gomez December 10, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
David Taylor
David Taylor April 21, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Anthony Martin
Anthony Martin March 13, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Cynthia  Davis
Cynthia Davis June 22, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Michael Perez
Michael Perez May 22, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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