Yunqing Tang is a mathematician specialising 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 ...

and

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 an assistant professor at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

. She was awarded the

SASTRA Ramanujan Prize The SASTRA Ramanujan Prize is an annual prize awarded to outstanding contributions in mathematics. It was incorporated and is awarded by the Shanmugha Arts, Science, Technology & Research Academy (SASTRA) in Thanjavur district, Tamil Nadu. The awa ...

in 2022 for "having established, by herself and in collaboration, a number of striking results on some central problems in arithmetic geometry and number theory". Yunqing Tang was born in China and secured a BSc degree from

Beijing University Peking University (PKU) is a public university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of China. The university is part of Project 211, Project 985, and the Double First-Class Construction. It i ...

in 2011 and then moved to

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 ...

for higher education, from where she graduated with a PhD degree in 2016 under the guidance of Mark Kisin. She was associated with

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 ...

in several capacities. First she was with the IAS Princeton during 2016-2017, then as an instructor from July 2017 to Jan 2020 and then as an assistant professor from July 2021 to June 2022, In between, she worked as a researcher at

CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

from February 2020 to June 2021. She is with University of California, Berkeley since July 2022.

Work

In collaboration with Vesselin Dimitrov and Frank Calegari, Tang proved the unbounded denominators conjecture of A.O.L. Atkin and Swinnerton-Dyer: if a modular form is not modular for some

congruence subgroup In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of invertible integer matrices of determinant 1 in which the off-diag ...

of the

modular group In mathematics, the modular group is the projective special linear group \operatorname(2,\mathbb Z) of 2\times 2 matrices with integer coefficients and determinant 1, such that the matrices A and -A are identified. The modular group acts on ...

, then the Fourier coefficients of have unbounded denominators. It has been known for decades that if is modular for some congruence subgroup, then its coefficients have bounded denominators. Also in collaboration with Dimitrov and Calegari, she proved the linear independence of

1, \zeta(2),

and

L(2,\chi_).

The citation for SASTRA Ramnujan Prize summarizes Yunqing Tang's contributions to mathematics thus: :"The prize notes that her works display a remarkable combination of sophisticated techniques, in which the arithmetic and geometry of modular curves and of Shimura varieties play a central role, and have strong links with the discoveries of Srinivasa Ramanujan in the area of modular equations. ... she established a new special case of the Ogus conjecture concerning cycles in de Rham cohomology of abelian varieties. She has shown that any abelian surface with real multiplication has infinitely many primes with split reduction. She resolved the long-standing unbounded denominators conjecture of Atkin and Swinnerton-Dyer that algebraic functions which are not invariant under any congruence subgroup of SL2(Z), must have unbounded denominators. The study of algebraic functions that are related to the moduli of elliptic integrals, stems from Ramanujan’s own investigations and the plethora of beautiful modular identities that he discovered."

Awards and recognition

The awards and recognition conferred on Yunqing Tang include: * AWM–Microsoft Research Prize in Algebra and Number Theory, 2024 *SASTRA Ramanujan Prize, 2022. *AWM Dissertation Prize, awarded for outstanding Ph.D dissertations by female students in the US, 2016. *New World Mathematics Award, Gold Medal for Ph.D thesis awarded for outstanding Chinese mathematics students worldwide, 2016. *Merit Research Fellowship, Graduate School of Arts and Sciences, Harvard University, 2015 – 2016.

References

{{reflist Recipients of the SASTRA Ramanujan Prize Living people Year of birth missing (living people) University of California, Berkeley faculty Peking University alumni Princeton University faculty Harvard University alumni