Xinyi Yuan ( zh, c=袁新意; born 1981) is a Chinese mathematician who is currently a professor of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

Peking University Peking University (PKU) is a Public university, public Types of universities and colleges in China#By designated academic emphasis, university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of the Peop ...

working in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

, and

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

s. In particular, his work focuses on arithmetic intersection theory, algebraic dynamics,

Diophantine equation ''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real n ...

s and special values of

L-functions In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may gi ...

Early life and education

Yuan is from

Macheng Macheng () is a city in northeastern Hubei province, People's Republic of China, bordering the provinces of Henan to the north and Anhui to the northeast. It is a county-level city under the administration of Huanggang City and abuts the south sid ...

Huanggang Huanggang is a prefecture-level city in easternmost Hubei, Hubei Province, China. It is situated to the north of the middle reaches of the Yangtze River and is bounded in the north by the Dabie Mountains and is named after Mount Huanggang, Huang ...

Hubei Hubei is a province of China, province in Central China. It has the List of Chinese provincial-level divisions by GDP, seventh-largest economy among Chinese provinces, the second-largest within Central China, and the third-largest among inland ...

province, and graduated from

Huanggang Middle School Huangzhou District is an urban district of Huanggang, Hubei province, China. History In 845 BC Marquis Wen 文侯 Huang Meng 黃孟 (aka Huang Zhang 黃璋) moved the capital of the State of Huang from Yicheng to Huangchuan (present-day Huang ...

in 2000. That year, he received a gold medal at the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

while representing

China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...

. Yuan obtained his A.B. in mathematics from

in 2003 and his Ph.D. in mathematics from the

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

in 2008 under the direction of Shou-Wu Zhang. His article "Big Line Bundles over Arithmetic Varieties," published in

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

, demonstrates a natural sufficient condition for when the

orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...

under the

absolute Galois group In mathematics, the absolute Galois group ''GK'' of a field ''K'' is the Galois group of ''K''sep over ''K'', where ''K''sep is a separable closure of ''K''. Alternatively it is the group of all automorphisms of the algebraic closure of ''K'' ...

is equidistributed.

Career

He spent time at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

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 ...

, and

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

before joining the Berkeley faculty in 2012. Yuan was appointed a Clay Research Fellow for a three-year term from 2008 to 2013. Together with a number of other collaborators, Yuan was profiled in

Quanta Magazine ''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. History ''Quanta Magazine'' was initially launched as ''Simons Science ...

and

Business Insider ''Business Insider'' (stylized in all caps: BUSINESS INSIDER; known from 2021 to 2023 as INSIDER) is a New York City–based multinational financial and business news website founded in 2007. Since 2015, a majority stake in ''Business Inside ...

for, among other things, his research on L-functions. Yuan left UC Berkeley to become a full professor at

in 2020.

Research

Together with Shou-Wu Zhang, Yuan proved the averaged Colmez conjecture which was later shown to imply the André–Oort conjecture for Siegel modular varieties by

Jacob Tsimerman Jacob Tsimerman (born 1988) is a Canadian mathematician at the University of Toronto specialising in number theory and related areas. He was awarded the SASTRA Ramanujan Prize in the year 2015 in recognition for his work on the André–Oort co ...

Publications (selected)

* (with Tong Zhang
"Effective Bound of Linear Series on Arithmetic Surfaces"

Duke Mathematical Journal ''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue inclu ...

162 (2013), no. 10, 1723–1770.
"On Volumes of Arithmetic Line Bundles"

Compositio Mathematica ''Compositio Mathematica'' is a monthly peer-reviewed mathematics journal established by L.E.J. Brouwer in 1935. It is owned by the Foundation Compositio Mathematica, and since 2004 it has been published on behalf of the Foundation by the London ...

145 (2009), 1447–1464.
"Big Line Bundles over Arithmetic Varieties"

Inventiones mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

173 (2008), no. 3, 603–649. * (with Tong Zhang
"Relative Noether inequality on fibered surfaces"

Advances in Mathematics ''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed ...

259 (2014), 89–115. * (with Shou-Wu Zhang
"The arithmetic Hodge index theorem for adelic line bundles"
,

Mathematische Annalen ''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, ...

(2016), 1–49. * (with Wei Zhang, Shou-Wu Zhang
"The Gross–Kohnen–Zagier theorem over totally real fields"

145 (2009), no. 5, 1147–1162. * (with Wei Zhang, Shou-Wu Zhang
"The Gross–Zagier formula on Shimura curves"
Annals of Mathematics Studies vol. 184, Princeton University Press, 2012. * (with Wei Zhang, Shou-Wu Zhang
"Triple product L-series and Gross–Kudla–Schoen cycles"
, preprint. *

References

{{DEFAULTSORT:Yuan, Xinyi Mathematicians from Hubei Living people University of California, Berkeley faculty Institute for Advanced Study visiting scholars Peking University alumni International Mathematical Olympiad participants People from Huanggang Educators from Hubei Arithmetic geometers 1981 births