Encyclopedia of Knot Theory
暫譯: 結繩理論百科全書

「結繩理論是一個迷人的數學主題，與理論物理有多重聯繫。這本百科全書充滿了關於這個豐富而迷人的主題的寶貴資訊。」
- Ed Witten，菲爾茲獎得主

「我花了一個愉快的下午瀏覽《結繩理論百科全書》。這是一部對該領域的古典和現代發展進行清晰介紹的綜合性編纂。對於成就卓越的研究者來說，這將是一個極好的資源，同時也將是吸引研究生和本科生進入該領域的絕佳方式。」
- Abigail Thompson，加州大學戴維斯分校數學特聘教授

結繩理論被證明是一個迷人的數學研究領域，歷史可追溯至約150年前。《結繩理論百科全書》提供了關於結繩理論各種活躍領域的短篇相互關聯的文章，並包含美麗的圖片、深刻的數學聯繫和重要的應用。本書中的許多文章對於正在進行研究或修習結繩理論高級本科課程的本科生來說都是可接觸的。更高級的文章將對於從事相關論文主題的研究生、對結繩理論當前結果感興趣的其他拓撲領域研究者，以及研究生物聚合物的拓撲和幾何的科學家們都將是有用的。

特點
- 提供對本科生、研究生和全職研究人員有用且易於接觸的材料
- 討論的主題為學生探索有意義的研究提供了極好的催化劑，並增強了他們追求高級學位的信心和承諾
- 由結繩理論領域的頂尖研究者編輯和貢獻

Colin Adams is the Thomas T. Read Professor of Mathematics at Williams College, having received his Ph.D. from the University of Wisconsin-Madison in 1983 and his Bachelor of Science from MIT in 1978.　 He is the author or co-author of numerous research papers in knot theory and low-dimensional topology and nine books, including the text The Knot Book", the comic book Why Knot? and the text　Introduction to Topology: Pure and Applied. He is a managing editor for the Journal of Knot Theory and its Ramifications and an editor for the recently publishedcKnots, Low Dimensional Topology and Applications, Springer, 2019. A　recipient of the Haimo National Distinguished Teaching Award, he has also been an MAA Polya Lecturer, a Sigma Xi Distinguished Lecturer, and a recipient of the Robert Foster Cherry Teaching Award. He has worked with over 130 undergraduates on original research in knot theory and low-dimensional topology.

He is also the humor columnist for the expository math magazine, the Mathematical Intelligencer.

Erica Flapan was a professor at Pomona College from 1986 to 2018. From 2000 until 2014, Flapan taught at the Summer Mathematics Program for freshmen and sophomore women at Carleton College, and mentored many of those women as they got their PhD's in mathematics. In 2011, Flapan won the Mathematical Association of America's Haimo award for distinguished college or university teaching of mathematics. Then in 2012, she was selected as an inaugural fellow of the American Mathematical Society. From 2015-2017, she was a Polya Lecturer for the MAA. Since 2019, she has been the Editor-in-Chief of the Notices of the American Mathematical Society.

Erica Flapan has published extensively in topology and its applications to chemistry and molecular biology. In addition to her many research papers, she has published an article in the College Mathematics Journal entitled "How to be a good teacher is an undecidable problem," as well as four books. Her first book, entitled When Topology Meets Chemistry was published jointly by the Mathematical Association of America and Cambridge University Press. Her second book entitled Applications of Knot Theory, is a collection of articles that Flapan co-edited with Professor Dorothy Buck of Imperial College London. Flapan also co-authored a textbook entitled Number Theory: A Lively Introduction with Proofs, Applications, and Stories with James Pommersheim and Tim Marks, published by John Wiley and sons. Finally, in 2016, the AMS published her book entitled Knots, Molecules, and the Universe: An Introduction to Topology, which is aimed at first and second year college students.

Allison Henrich is a Professor of Mathematics at Seattle University. She earned her PhD in Mathematics from Dartmouth College in 2008 and her undergraduate degrees in Mathematics and Philosophy from the University of Washington in 2003. Allison has been dedicated to providing undergraduates with high-quality research experiences since she mentored her first group of students in the SMALL REU at Williams College in 2009, under the mentorship of Colin Adams. Since then, she has mentored 35 beginning researchers, both undergraduates and high school students. She has directed and mentored students in the SUMmER REU at Seattle University and has served as a councilor on the Council on Undergraduate Research. In addition, Allison co-authored An Interactive Introduction to Knot Theory for undergraduates interested in exploring knots with a researcher's mindset, and she co-authored A Mathematician's Practical Guide to Mentoring Undergraduate Research, a resource for math faculty. Allison is excited about the publication of the Concise Encyclopedia of Knot Theory, as it will be an essential resource for beginning knot theory researchers!

Louis H. Kauffman was born in Potsdam, New York on Feb. 3, 1945. As a teenager he developed interests in Boolean algebra, circuits, diagrammatic logic and experiments related to non-linear pendulum oscillations. He received the degree of B.S. in Mathematics from MIT in 1966 and went to Princeton University for graduate school where he was awarded PhD in 1972. At Princeton he studied with William Browder and began working with knots and with singularities of complex hypersurfaces through conversations with the knot theorist Ralph Fox and the lectures of F. Hirzebruch and J. Milnor. From January 1971 to May 2017, he taught at the University of Illinois at Chicago where he is now Emeritus Professor of Mathematics.

Kauffman's research is in algebraic topology and particularly in low dimensional topology (knot theory) and its relationships with algebra, logic, combinatorics, mathematical physics and natural science. He is particularly interested in the structure of formal diagrammatic systems such as the system of knot diagrams that is one of the foundational approaches to knot theory. Kauffman's research in Virtual Knot Theory has opened a new field of knot theory and has resulted in the discovery of new invariants of knots and links. His work on Temperley-Lieb Recoupling Theory with Sostences Lins led to new approaches to the Fibonacci model (Kitaev) for topological quantum computing. He has recently worked on representations of the Artin braid group related to the structure of Majorana Fermions.

His interdisciplinary research on cybernetics is concentrated on foundational understanding of mathematics based in the act of distinction, recursion and eigenform (the general structure of fixed points). This research is important both for mathematics and for the connections that are revealed in cybernetics with many other fields of study including the understanding of cognition, language, social systems and natural science.

Kauffman is the author of four books on knot theory, a book on map coloring and the reformulation of mathematical problems, Map Reformulation (Princelet Editions; London and Zurich [1986]) and is the editor of the World-Scientific Book Series On Knots and Everything. He is the Editor-in-Chief and founding editor of the Journal of Knot Theory and Its Ramifications. He is the co-editor of the review volume (with R. Baadhio) Quantum Topology and editor of the review volume Knots and Applications, both published by World Scientific Press and other review volumes in the Series on Knots and Everything.

Kauffman is the recipient of a 1993 University Scholar Award by the University of Illinois at Chicago. He was also awarded Warren McCulloch Memorial Award of the American Society for Cybernetics for significant contributions to the field of Cybernetics in the same year. He has also been awarded the 1996 award of the Alternative Natural Philosophy Association for his contribution to the understanding of discrete physics and the 2014 Norbert Wiener Medal from the American Society for Cybernetics. He was the president of the American Society for Cybernetics from 2005-2008 and the former Polya Lecturer for MAA (2008-2010). He was elected a Fellow of the American Mathematical Society in 2014.

Kauffman writes a column "Virtual Logic" for the Journal Cybernetics and Human Knowing and he plays clarinet in the Chicago-based ChickenFat Klezmer Orchestra.

Lewis D. Ludwig is a professor of mathematics at Denison University. He holds a PhD and Master's in Mathematics from Ohio University and Miami University. His research in the field of topology mainly focuses on knot theory, a study in which he engages undergraduate students; nearly a third of his publications involve undergraduate collaborators. Lew created and co-hosted the　Undergraduate　Knot　Theory　Conference,　the　UnKnot Conference, at Denison University which cumulatively supported over 300 undergraduate students, their faculty mentors, and researchers. Lew was a Co-PI and Project Team coordinator for the　MAA Instructional Practices Guide Project　- a guide to evidence-based instructional practices in undergraduate mathematics. He was creator and senior-editor for　Teaching Tidbits　blog for the MAA, a blog which provided techniques on evidence- based active teaching strategies for mathematics. Lew won the Distinguished Teaching Award for the Ohio Section of the MAA in 2013 and held the Nancy Eshelman Brickman Endowed Professorship.

Sam Nelson is a Professor and Chair of the Department of Mathematical Sciences at Claremont McKenna College. He earned his PhD in Mathematics at Louisiana State University in 2002 and his BS in Mathematics with minor in Philosophy at the University of Wyoming in 1996. A member of UWyo's first cohort of McNair Scholars, he has published 75 papers including over 40 with undergraduate and high school student co-authors, and is co-author of Quandles: An Introduction to the Algebra of Knots, the first textbook on Quandle theory. He has served as the Section Chair of the SoCal-Nevada section of the Mathematical Association of America and is an active member of the Mathematical Society of Japan and the American Mathematical Society, where he has co-organized 17 special sessions on Algebraic Structures in Knot Theory. He sits on the editorial boards of the Journal of Knot Theory and its Ramifications and the Communications of the Korean Mathematical Society, is the recipient of two Simons Foundation Collaboration grants, and was recently honoured as the recipient of Claremont McKenna College's annual Faculty Research Award. When not doing mathematics, he creates electronic music from knot diagrams as independent artist and composer Modulo Torsion.

**Colin Adams** 是威廉斯學院的托馬斯·T·瑞德數學教授，於1983年在威斯康辛大學麥迪遜分校獲得博士學位，並於1978年在麻省理工學院獲得理學士學位。他是多篇有關結理論和低維拓撲的研究論文的作者或合著者，並著有九本書籍，包括《The Knot Book》、漫畫書《Why Knot?》以及《Introduction to Topology: Pure and Applied》。他是《Journal of Knot Theory and its Ramifications》的主編，並擔任最近出版的《Knots, Low Dimensional Topology and Applications》的編輯（施普林格，2019年）。作為海默國家傑出教學獎的獲得者，他曾擔任MAA的波利亞講者、Sigma Xi的傑出講者，以及羅伯特·福斯特·切瑞教學獎的獲得者。他與超過130名本科生合作進行結理論和低維拓撲的原創研究。

他也是數學普及雜誌《Mathematical Intelligencer》的幽默專欄作家。

**Erica Flapan** 於1986年至2018年擔任波莫納學院的教授。從2000年到2014年，Flapan在卡爾頓學院的夏季數學計劃中教授大一和大二的女性學生，並指導許多這些女性獲得數學博士學位。2011年，Flapan因其在數學教學方面的傑出貢獻獲得美國數學協會的海默獎。2012年，她被選為美國數學學會的首批研究員之一。2015年至2017年，她擔任MAA的波利亞講者。自2019年以來，她一直是美國數學學會通報的主編。

Erica Flapan在拓撲學及其在化學和分子生物學中的應用方面發表了大量研究。除了她的多篇研究論文外，她還在《College Mathematics Journal》上發表了一篇題為《How to be a good teacher is an undecidable problem》的文章，以及四本書。她的第一本書《When Topology Meets Chemistry》由美國數學協會和劍橋大學出版社共同出版。她的第二本書《Applications of Knot Theory》是Flapan與倫敦帝國學院的Dorothy Buck教授共同編輯的文章集。Flapan還與James Pommersheim和Tim Marks共同撰寫了一本教科書《Number Theory: A Lively Introduction with Proofs, Applications, and Stories》，由約翰·威利和兒子出版。最後，在2016年，AMS出版了她的書《Knots, Molecules, and the Universe: An Introduction to Topology》，該書旨在幫助大一和大二的學生。

**Allison Henrich** 是西雅圖大學的數學教授。她於2008年在達特茅斯學院獲得數學博士學位，並於2003年在華盛頓大學獲得數學和哲學的學士學位。自2009年在威廉斯學院的SMALL REU指導她的第一組學生以來，Allison一直致力於為本科生提供高質量的研究經驗。自那時以來，她已指導了35名初學研究者，包括本科生和高中生。她在西雅圖大學的SUMmER REU中指導和指導學生，並擔任本科研究委員會的顧問。此外，Allison共同撰寫了《An Interactive Introduction to Knot Theory》，旨在幫助對結有研究興趣的本科生，並共同撰寫了《A Mathematician's Practical Guide to Mentoring Undergraduate Research》，這是一本為數學教師提供的資源。Allison對《Concise Encyclopedia of Knot Theory》的出版感到興奮，因為這將成為初學結理論研究者的重要資源！

**Louis H. Kauffman** 於1945年2月3日出生於紐約州的波茨坦。作為青少年，他對布爾代數、電路、圖示邏輯以及與非線性擺動相關的實驗產生了興趣。他於1966年在麻省理工學院獲得數學學士學位，並前往普林斯頓大學攻讀研究生學位，於1972年獲得博士學位。在普林斯頓，他與William Browder學習，並通過與結理論家Ralph Fox的對話以及F. Hirzebruch和J. Milnor的講座開始研究結和複超曲面的奇異性。從1971年1月到2017年5月，他在伊利諾伊大學芝加哥分校任教，現在是數學榮譽教授。

Kauffman的研究集中在代數拓撲，特別是低維拓撲（結理論）及其與代數、邏輯、組合學、數學物理和自然科學的關係。他特別對形式圖示系統的結構感興趣，例如結圖的系統，這是結理論的基礎方法之一。Kauffman在虛擬結理論的研究開創了一個新的結理論領域，並發現了結和鏈的新不變量。他與Sostences Lins合作的Temperley-Lieb重耦合理論為拓撲量子計算的Fibonacci模型（Kitaev）提供了新的方法。他最近在與Majorana費米子結構相關的Artin編織群的表示方面進行了研究。

他在控制論的跨學科研究集中於基於區分、遞歸和特徵形式（不動點的一般結構）的數學基礎理解。這項研究對數學以及控制論與許多其他研究領域（包括認知、語言、社會系統和自然科學的理解）之間的聯繫都很重要。

Kauffman是四本有關結理論的書籍的作者，還有一本關於地圖著色和數學問題重構的書《Map Reformulation》（Princelet Editions; 倫敦和蘇黎世 [1986]），並且是世界科學出版社的《On Knots and Everything》系列的編輯。他是《Journal of Knot Theory and Its Ramifications》的主編和創始編輯。他還是評論卷的共同編輯（與R. Baadhio）《Quantum Topology》，以及評論卷《Knots and Applications》的編輯，這些都是由世界科學出版社出版的，還有其他在《Knots and Everything》系列中的評論卷。

Kauffman於1993年獲得伊利諾伊大學芝加哥分校的學者獎。同年，他還因對控制論領域的重大貢獻而獲得美國控制論學會的Warren McCulloch紀念獎。他還因對離散物理理解的貢獻而獲得1996年替代自然哲學協會的獎項，以及2014年美國控制論學會的Norbert Wiener獎。他於2005年至2008年擔任美國控制論學會的會長，並曾擔任MAA的波利亞講者（2008-2010）。他於2014年被選為美國數學學會的會士。

Kauffman為《Cybernetics and Human Knowing》期刊撰寫專欄《Virtual Logic》，並在芝加哥的ChickenFat Klezmer Orchestra中演奏單簧管。

**Lewis D. Ludwig** 是丹尼森大學的數學教授。他擁有俄亥俄大學和邁阿密大學的數學博士和碩士學位。他在拓撲學領域的研究主要集中在結理論，這是一個他與本科生共同參與的研究領域；他的近三分之一的出版物涉及本科生合作者。Lew創建並共同主持了丹尼森大學的**Un**dergraduate **Knot** Theory **Conference**，即UnKnot會議，累計支持了超過300名本科生及其教師導師和研究人員。Lew是MAA教學實踐指南項目的共同首席研究員和項目團隊協調員，該指南提供了基於證據的本科數學教學實踐。他還是MAA的Teaching Tidbits博客的創建者和高級編輯，該博客提供了基於證據的數學主動教學策略的技術。Lew於2013年獲得MAA俄亥俄分會的傑出教學獎，並擔任Nancy Eshelman Brickman講座教授。

**Sam Nelson** 是克萊蒙特·麥肯納學院數學科學系的教授和系主任。他於2002年在路易斯安那州立大學獲得數學博士學位，並於1996年在懷俄明大學獲得數學學士學位，輔修哲學。作為懷俄明大學第一屆McNair學者的成員，他發表了75篇論文，其中超過40篇與本科生和高中生共同作者，並且是《Quandles: An Introduction to the Algebra of Knots》的共同作者，這是第一本關於Quandle理論的教科書。他曾擔任美國數學協會南加州-內華達分會的分會主席，並且是日本數學學會和美國數學學會的活躍成員，在那裡他共同組織了17個有關結理論中的代數結構的特別會議。他是《Journal of Knot Theory and its Ramifications》和《Communications of the Korean Mathematical Society》的編輯委員會成員，獲得了兩項Simons基金會的合作獎勵，並最近被克萊蒙特·麥肯納學院授予年度教職員研究獎。當不從事數學時，他作為獨立藝術家和作曲家Modulo Torsion創作基於結圖的電子音樂。