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
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 ...
. 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
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 "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
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 ...
, 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
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 ...
, 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)