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

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

and

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s. A professor at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...

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 founded in 1961 in memory of Oswald Veblen. The Veblen Prize is now worth US$5000, and is ...

in 2019. In 2019, he was awarded the

Simons Investigator The Simons Foundation is a private foundation established in 1994 by Marilyn and Jim Simons with offices in New York City. As one of the largest charitable organizations in the US with assets of over $5 billion in 2022, the foundation's mission ...

award.

Biography

Chen was born in

Qingtian County Qingtian (), is a county in southeastern Zhejiang Province, on the middle-lower reaches of the Ou River which flows 388 kilometers (241 mi) before finally reaching the city of Wenzhou and emptying into the East China Sea. The county is known ...

Zhejiang Zhejiang ( or , ; , also romanized as Chekiang) is an eastern, coastal province of the People's Republic of China. Its capital and largest city is Hangzhou, and other notable cities include Ningbo and Wenzhou. Zhejiang is bordered by Jiang ...

, China. He entered the Department of Mathematics of the

University of Science and Technology of China A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

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 (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

. The last doctoral student of

Eugenio Calabi Eugenio Calabi (born 11 May 1923) is an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics, Emeritus, at the University of Pennsylvania, specializing in differential geometry, partial differential equations and ...

, 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 and Westdale, adjacent to the Royal Botanical Ga ...

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

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

postdoctoral fellow at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

. He was an assistant professor at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

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

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

. 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 Song Sun (, born in 1987) is a Chinese mathematician whose research concerns geometry and topology. A Sloan Research Fellow, he is a professor at the Department of Mathematics of the University of California, Berkeley, where he has been since 2018 ...

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 Nevanlinna Prize (to be rename ...

, in Beijing.

Conjecture on Fano manifolds and Veblen Prize

In 2019, Chen was awarded the prestigious

, together with

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

and Chen's former student

, for proving a long-standing conjecture on

Fano manifolds In algebraic geometry, a Fano variety, introduced by Gino Fano in , is a complete variety ''X'' whose anticanonical bundle ''K''X* is ample. In this definition, one could assume that ''X'' is smooth over a field, but the minimal model program has ...

, 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 mo ...

if and only if it is K-stable". It had been one of the most actively investigated topics in geometry since its proposal in the 1980s by

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathem ...

after he proved 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 ...

. It was later generalized by

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 abstr ...

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