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本卷匯集了十四篇由印度傑出數學家撰寫的論文，提供了當前數學研究方向以及印度數學最近歷史發展的全景視角。這些文章涵蓋了多樣的主題——數論、算子代數、算子理論、調和分析、量子學習、非交換幾何和隨機矩陣——展示了當代數學研究的廣度和深度。本書生動地描繪了當今數學思想的演變，將傳統與創新相連接，並為下一代數學家提供了洞見和靈感。
本卷以M. S. Raghunathan的啟發性文章《20世紀印度對數學的貢獻亮點》開篇，這是一篇全面的歷史回顧，講述了印度獨立後的數學研究，將激勵年輕讀者和學者。特別收錄的研究文章是Kyoung-Seog Lee和已故的M. S. Narasimhan共同撰寫的《曲線上向量束的對稱乘積和模空間》，該論文在Narasimhan於2021年去世前不久完成。這篇已在研究界引起廣泛關注的論文，成為對他在代數幾何領域持久影響的恰當致敬。
作者簡介
Gadadhar Misra is currently Visiting Professor in the Department of Mathematics at the Indian Institute of Technology Gandhinagar, Gujarat. He previously served as Professor and Chair of the Department of Mathematics at the Indian Institute of Science (IISc), Bengaluru, and as Head of the Indian Statistical Institute, Bangalore Centre. A distinguished mathematician, inspiring teacher and active researcher, he is a Fellow of the Indian Academy of Sciences, the Indian National Science Academy (where he served as Vice President, 2018-2020), and the National Academy of Sciences, India. He was also a recipient of the J. C. Bose Fellowship (2008-2023). Besides, he received the Shanti Swarup Bhatnagar Prize (2001) and the Biju Patnaik Award for Scientific Excellence (2013), awarded by the Odisha Bigyan Academy in recognition of his outstanding research and academic contributions.
His research interests lie in operator theory, functional analysis and Hilbert modules, and he has played a major role in promoting collaborative research and strengthening mathematics education in India. After completing his master's degree from Sambalpur University, he earned his Ph.D. under the supervision of Prof. Ronald G. Douglas at Stony Brook University, USA. His dissertation, "Curvature Inequalities and External Properties of Bundle Shifts", set the course for a career devoted to deep mathematical inquiry. He has collaborated with several eminent mathematicians and young researchers alike, contributing notably to the study of homogeneous operators, Hilbert modules and geometric invariants of quotient modules. He has published extensively in leading national and international journals and has supervised numerous doctoral students.作者簡介(中文翻譯)
加達哈爾·米斯拉目前擔任印度理工學院甘地納格爾數學系的訪問教授。他曾擔任印度科學研究院（IISc）班加羅爾數學系的教授及系主任，以及印度統計學院班加羅爾中心的主任。作為一位傑出的數學家、啟發人心的教師和活躍的研究者，他是印度科學院、印度國家科學院（曾於2018-2020年擔任副院長）和印度科學院的院士。他還曾獲得J. C. Bose獎學金（2008-2023）。此外，他獲得了香提·斯瓦魯普·巴特納加獎（2001）和比朱·帕特奈克科學卓越獎（2013），該獎項由奧迪沙大學院頒發，以表彰他在研究和學術貢獻方面的卓越表現。
他的研究興趣包括算子理論、泛函分析和希爾伯特模塊，他在促進合作研究和加強印度數學教育方面發揮了重要作用。在完成桑巴爾普爾大學的碩士學位後，他在美國石溪大學的羅納德·G·道格拉斯教授指導下獲得博士學位。他的論文《曲率不等式與束移的外部性質》為他致力於深入數學研究的職業生涯奠定了基礎。他與多位傑出的數學家和年輕研究者合作，對均勻算子、希爾伯特模塊和商模塊的幾何不變量的研究做出了顯著貢獻。他在國內外主要期刊上發表了大量論文，並指導了許多博士生。
