美國數學學會官網顯示，2021年度科爾代數獎授予許晨陽，表彰他對K-穩定Fano簇的模空間理論以及使用K-穩定性研究極小模型綱領中的奇點的貢獻。
該獎項嘉許以下論文:
[1] C. Hacon, J. McKernan and C. Xu, 「Boundedness of moduli of varieties of general type,」 J. Euro. Math. Soc. 20 (2018), Issue 4, 865–901.
[2] C. Li, X. Wang and C. Xu, 「On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties,」 Duke Math. J. 168 (2019), 1387–1459.
[3] H. Blum and C. Xu, 「Uniqueness of K-polystable degenerations of Fano varieties,」 Annals of Math. 190 (2019), 609–656.
[4] C. Xu, 「A minimizing valuation is quasi-monomial,」 Annals of Math. 191 (2020), 1003–1030.
[5] J. Alper, H. Blum, D. Halpern-Leistner and C. Xu, 「Reductivity of the automorphism group of K-polystable Fano varieties,」 Invent. Math., to appear.
獲獎人簡介圖片來源作者主頁：https://web.math.princeton.edu/~chenyang/許晨陽1981年出生於重慶，本科就讀於北京大學，研究生就讀於普林斯頓大學，師從Janos Kollár。他在麻省理工學院(MIT)擔任博士後。2011年，許晨陽在猶他大學工作一年。他於2012年加入北京大學北京國際數學研究中心，並於2013年晉升為教授。2018年，他全職在麻省理工學院任教。2020年9月，他成為普林斯頓大學的教授。
許晨陽的主要研究領域是高維代數簇的雙有理幾何，他喜歡探索它與其他領域的聯繫，曾獲2016年度拉馬努金獎、2017年未來科學大獎——數學與計算機科學獎、2019新視野數學獎。
許晨陽的回應❝Constructing moduli spaces to parametrize objects has always been one of the most powerful tools in algebraic geometry. D. Mumford settled the case in dimension one for curves. This was later vastly generalized to higher dimension to parametrize varieties with a negative Chern class, via the Kollár-Shepherd-Barron program, which has been an intellectual engine in higher-dimensional geometry since the late 『80s, whose development intertwines with the minimal model program started by S. Mori.
It has been mysterious to algebraic geometers for a very long time how to construct a moduli space for varieties with a positive Chern class. Such varieties are called Fano varieties, named after the Italian mathematician G. Fano. After a period of experimental searching, it has eventually become clear that one can investigate the notion of K-stability defined by G. Tian and S. Donaldson to capture the existence of Kähler-Einstein metric, using the machinery from higher dimensional geometry, and build up a new field—the algebraic K-stability theory of Fano varieties. Then the moduli space of Fano varieties comes out of the theory, as the best reward. Under the local-to-global philosophy, one could expect a local K-stability theory for singularities, and such expectation is fulfilled by studying the geometry of the minimizer of the normalized volume function on the valuation space of a singularity, a picture far outside the scope of the traditional higher dimensional geometry.
I’m very glad that the committee recognized the field and I feel profoundly honored that they chose me to represent the area. It is still a relatively new area and I am very happy to see that there have been a number of young brilliant mathematicians working on it. I hope that the recognition by the Frank Nelson Cole Prize will spur further activities.
The Cole Prize gives me the precious opportunity to acknowledge the invaluable aid I have received from others. I would like to thank my advisor J. Kollár, who shaped my thinking of the moduli of higher dimensional varieties. I would like to thank C. Hacon and J. McKernan; through our collaborations I learned tremendously about the minimal model program. I also want to thank all my collaborators on this topic whom the recognition should also be associated with, especially C. Li and X. Wang, for suffering the pain together earlier when it was not clear to which direction the subject would move; as well as J. Alper, H. Blum, D. Halpern-Leistner, Y. Liu and Z. Zhuang, for their energy and ideas in our joint works. I want to thank Peking University, MIT and Princeton for providing me a wonderful environment to accomplish the research. Finally, I want to thank my family, especially my wife Xiaoyu, for her constant support.
❞拙譯如下：
構造模空間來參數化對象一直是代數幾何學中最強大的工具之一。D. Mumford解決了曲線的一維情況。後來，通過Kollár-Shepherd-Barron綱領，可以推廣到高維，將陳類為負的簇參數化，該綱領自 80 年代末以來一直是推動高維幾何學發展的引擎，其發展與森重文（S. Mori）開創的極小模型綱領交織在一起。
長期以來，對代數幾何學家而言，如何構造具有正陳類的簇的模空間一直是一個難題。這種簇被稱為Fano簇，以義大利數學家G. Fano的名字命名。經過一段時間的試驗探索，人們終於發現，能夠利用高維幾何學的工具研究由田剛和S. Donaldson定義的K-穩定性概念工具，可以得到Kähler-Einstein度量的存在性，並建立一個新的研究領域——Fano簇的代數K-穩定性理論。然後可以得到Fano簇的模空間理論。在局部-整體的哲學下，我們期待一個關於奇點的局部K-穩定性理論，它通過研究一個奇點的賦值空間上的最小化正則體積函數的幾何，這幅圖景遠遠超出傳統高維幾何範圍。
我很高興委員會認可了這個領域，並深感榮幸他們選擇了我作為這個領域的代表。它仍然是一個相對較新的領域，我很高興看到已經有許多年輕的傑出數學家從事這方面的工作。我希望科爾獎的認可能促進進一步的研究。
科爾獎給了我一個寶貴的機會來感謝我從其他人那裡得到的無價的幫助。我要感謝我的導師J. Kollár，他塑造了我對高維簇的模的思考。我要感謝C. Hacon和J.McKernan，通過我們的合作，我學到了關於極小模型綱領的大量知識。我還要感謝所有在這個課題上的合作者，尤其是李馳和王曉瑋，他們也應得到認可，因為在早期這個主題會往哪個方向發展時，他們一起忍受了痛苦。我還要感謝J. Alper, H. Blum, D. Halpern-Leistner, 劉雨晨和莊梓銓，因為他們在合作中提供的能量和想法。我要感謝北京大學、麻省理工學院和普林斯頓大學為我提供了一個完成研究的絕佳環境。最後，我要感謝我的家人，特別是我的妻子Xiaoyu的一如既往的支持。
關於科爾代數獎科爾代數獎每三年頒發一次，嘉獎在過去六年中出現的著名代數研究成果。該獎項和科爾數論獎於1928年設立，以紀念弗蘭克·尼爾森·科爾(1861-1926)。