Geometric Methods in Physics XXXIX: Workshop, Bialystok, Poland, 2022

本卷彙集了在2022年6月於波蘭比亞維斯托克舉行的第XXXIX屆幾何方法在物理學研討會上所發表的講座論文。這些章節為讀者提供了幾何學、分析及其他多個領域前沿研究的概覽。具體主題包括：
- 古典與量子場論
- 無限維群
- 可積系統
- 李群體與李代數體
- 表示論

《幾何方法在物理學 XXXIX》將成為對於數學家和物理學家在這些領域交集的最新發展感興趣的寶貴資源。

Dr. Piotr Kielanowski is a professor of theoretical and mathematical physics at the Center for Research and Advanced Studies of the Polytechnic University of Mexico in Mexico City. He has published more than 80 original papers in the field of particle phenomenology and has mentored several PhD students. He is the co-author of a book on quantum mechanics (Quantum Physics: States, Observables and Their Time Evolution, Springer, 2019). He has been a member of the Organizing Committee of the Bialowieża Workshop on Geometric Methods in Physics for about 20 years, and has been the editor of successive volumes of the proceedings.

Dr. Alina Dobrogowska is a professor in the Faculty of Mathematics of the University of Bialystok, Poland. She has published numerous papers on integrable systems, particularly in relation to factorization methods, bihamiltonian systems, q-difference equations and Lie algebroids. She has been a member of the Organizing Committee of the Workshopsince 2001, and since last year she is the chairman of the Organizing Committee.

Dr. Gerald A. Goldin is a distinguished professor of mathematics, physics, and mathematics education at Rutgers University in New Brunswick, New Jersey. His work in mathematical physics focuses on local current algebras and their representations, measures on infinite-dimensional configuration spaces, quantum vortex configurations, nonlinear electrodynamics, and nonlinear variations of quantum mechanics. With colleagues at Los Alamos National Laboratory, he was an early co-discoverer of the possibility of "anyon" and "nonabelian anyon" statistics. He is a recipient of the Alexander von Humboldt Research Prize in physics, and has been a Workshop participant for over 30 years.

Dr. Tomasz Goliński is an assistant professor in the Faculty of Mathematics of the University of Bialystok, Poland. His research interests address various aspects of mathematical physics, with emphasis on topics related to problems of functional analysis and operator algebras. These include infinite dimensional geometry with emphasis on Poisson geometry on Banach manifolds, Banach Lie groupoids and algebroids, integrable systems, and factorization methods in their discrete version. He has been Secretary of the Workshop since 2003.

Dr. Piotr Kielanowski 是墨西哥城墨西哥理工大學研究與進階研究中心的理論與數學物理教授。他在粒子現象學領域發表了超過80篇原創論文，並指導了多位博士生。他是一本關於量子力學的書籍（《Quantum Physics: States, Observables and Their Time Evolution》，Springer，2019）的共同作者。他已經擔任比亞瓦維斯卡幾何方法物理研討會的組織委員會成員約20年，並且一直是會議論文集的編輯。

Dr. Alina Dobrogowska 是波蘭比亞維斯托克大學數學系的教授。她在可積系統方面發表了大量論文，特別是與因式分解方法、雙哈密頓系統、q-差分方程和李代數體系相關的研究。自2001年以來，她一直是研討會的組織委員會成員，並且自去年起擔任組織委員會主席。

Dr. Gerald A. Goldin 是新澤西州新布倫瑞克的羅格斯大學數學、物理及數學教育的傑出教授。他在數學物理方面的研究專注於局部電流代數及其表示、無限維配置空間上的測度、量子漩渦配置、非線性電動力學以及量子力學的非線性變分。與洛斯阿拉莫斯國家實驗室的同事們一起，他是早期共同發現「anyon」和「非阿貝爾anyon」統計可能性的研究者之一。他是亞歷山大·馮·洪堡物理研究獎的獲得者，並且參加研討會已超過30年。

Dr. Tomasz Goliński 是波蘭比亞維斯托克大學數學系的助理教授。他的研究興趣涵蓋數學物理的各個方面，特別強調與泛函分析和算子代數問題相關的主題。這些主題包括無限維幾何，特別是巴拿赫流形上的泊松幾何、巴拿赫李群體和代數體系、可積系統以及其離散版本的因式分解方法。自2003年以來，他一直擔任研討會的秘書。