Xiuxiong Chen () is a Chinese-American mathematician whose research concerns

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and differential equations. Professor at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...

since 2010, he was elected a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2015 and awarded the

Oswald Veblen Prize in Geometry __NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is n ...

in 2019. In 2019, he was awarded the

Simons Investigator The Simons Foundation is an American private foundation established in 1994 by Marilyn and James Harris Simons, Jim Simons with offices in New York City. As one of the largest charitable organizations in the United States with assets of over $5 ...

award.

Biography

Chen was born in

Qingtian County Qingtian (), is a county located in the southeastern part of Lishui, Zhejiang, China. It is split in two by the Ou River, which flows 388 kilometers before finally reaching the city of Wenzhou and emptying into the East China Sea. The county has a ...

Zhejiang ) , translit_lang1_type2 = , translit_lang1_info2 = ( Hangzhounese) ( Ningbonese) (Wenzhounese) , image_skyline = 玉甑峰全貌 - panoramio.jpg , image_caption = View of the Yandang Mountains , image_map = Zhejiang i ...

, China. He entered the Department of Mathematics of the

University of Science and Technology of China The University of Science and Technology of China (USTC) is a public university in Hefei, China. It is affiliated with the Chinese Academy of Sciences, and co-funded by the Chinese Academy of Sciences, the Ministry of Education of the People' ...

in 1982, and graduated in 1987. He subsequently studied under Peng Jiagui (彭家贵) at the Graduate School of the Chinese Academy of Sciences, where he earned his master's degree. In 1989, he moved to the United States to study at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

. The last doctoral student of

Eugenio Calabi Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equa ...

, he obtained his Ph.D. in mathematics in 1994, with his dissertation on "Extremal

Hermitian Matrices In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th ...

with Curvature Distortion in a

Riemann Surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

". Chen was an instructor at

McMaster University McMaster University (McMaster or Mac) is a public research university in Hamilton, Ontario, Canada. The main McMaster campus is on of land near the residential neighbourhoods of Ainslie Wood, Ontario, Ainslie Wood and Westdale, Ontario, Westd ...

in Canada from 1994 to 1996. For the next two years he was a

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

postdoctoral fellow at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

. He was an assistant professor at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

from 1998 to 2002, before becoming an associate professor at the

University of Wisconsin–Madison The University of Wisconsin–Madison (University of Wisconsin, Wisconsin, UW, UW–Madison, or simply Madison) is a public land-grant research university in Madison, Wisconsin, United States. It was founded in 1848 when Wisconsin achieved st ...

. He was promoted to full professor in 2005. Since October 2010 he has been a professor at

. In 2006, he founded the Pacific Rim Conference on Complex Geometry at the University of Science and Technology of China. As of 2019, Chen has advised 17 Ph.D. students, including Song Sun and Bing Wang (王兵). He was elected a Fellow of the

in 2015 "for contributions to differential geometry, particularly the theory of extremal Kahler metrics". He was an invited speaker at the 2002

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

, in Beijing.

Conjecture on Fano manifolds and Veblen Prize

In 2019, Chen was awarded the prestigious

, together with English mathematician

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth function, smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähl ...

and Chen's former student Song Sun, for proving a long-standing conjecture on Fano manifolds, which states "that a Fano manifold admits a

Kähler–Einstein metric In differential geometry, a Kähler–Einstein metric on a complex manifold is a Riemannian metric that is both a Kähler metric and an Einstein metric. A manifold is said to be Kähler–Einstein if it admits a Kähler–Einstein metric. The ...

if and only if it is K-stable". It had been one of the most actively investigated topics in geometry since a loose version of it was first proposed in the 1980s by eventual

Fields Medalist The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar ...

after his proof of the

Calabi conjecture In the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on certain complex manifolds, made by . It was proved by , who received the Fields Medal and Oswa ...

. More precise versions were subsequently proposed by Chinese mathematician

Gang Tian Tian Gang (; born November 24, 1958) is a Chinese mathematician. He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University. He is known for contributions to the mathematical fields of Kähler g ...

and Donaldson. The solution by Chen, Donaldson and Sun was published in the ''

Journal of the American Mathematical Society The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abs ...

'' in 2015 as a three-article series, "Kähler–Einstein metrics on Fano manifolds, I, II and III".

Major publications

* Chen, Xiuxiong. ''The space of Kähler metrics.'' J. Differential Geom. 56 (2000), no. 2, 189–234. * Chen, X. X.; Tian, G. ''Geometry of Kähler metrics and foliations by holomorphic discs.'' Publ. Math. Inst. Hautes Études Sci. No. 107 (2008), 1–107. * Chen, Xiuxiong; Donaldson, Simon; Sun, Song. ''Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities.'' J. Amer. Math. Soc. 28 (2015), no. 1, 183–197. * Chen, Xiuxiong; Donaldson, Simon; Sun, Song. ''Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2π.'' J. Amer. Math. Soc. 28 (2015), no. 1, 199–234. * Chen, Xiuxiong; Donaldson, Simon; Sun, Song. ''Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof.'' J. Amer. Math. Soc. 28 (2015), no. 1, 235–278. * Chen, Xiuxiong; Wang, Bing. ''Space of Ricci flows (II)—Part B: Weak compactness of the flows.'' J. Differential Geom. 116 (2020), no. 1, 1 - 123. * Chen, Xiuxiong; Cheng, Jingrui. ''On the constant scalar curvature Kähler metrics (I)—A priori estimates.'' J. Amer. Math. Soc. 34 (2021), no. 4, 909–936. * Chen, Xiuxiong; Cheng, Jingrui. ''On the constant scalar curvature Kähler metrics (II)—Existence results.'' J. Amer. Math. Soc. 34 (2021), no. 4, 937–1009.

References

{{DEFAULTSORT:Chen, Xiuxiong Living people 21st-century American mathematicians Academic staff of McMaster University Chinese emigrants to the United States Differential geometers Fellows of the American Mathematical Society Mathematicians from Zhejiang People from Qingtian County Scientists from Lishui Princeton University faculty Stanford University postdoctoral scholars Stony Brook University faculty Simons Investigator University of the Chinese Academy of Sciences alumni University of Pennsylvania alumni University of Science and Technology of China alumni University of Wisconsin–Madison faculty Year of birth missing (living people)