Prof. Ruan Yongbin Elected as CAS Member in 2021

On November 18, the Chinese Academy of Sciences (CAS) unveiled the list of this year’s new members. Prof. Ruan Yongbin at the Institute for Advanced Study in Mathematics (IASM) was elected as CAS member. Congratulations! Prof. Ruan Yongbin has long committed himself to the research of symplectic geometry and mathematical physics. He has made significant contributions to Gromov-Witten invariants and quantum cohomology, Chen-Ruan cohomology, FJRW theory and their applications. Prof. Ruan obtained his Ph.D from UC-Berkeley in 1991. Afterwards, he was a postdoc at Michigan State University (1991-1993), an assistant professor at University of Utah (1993-1996), a Van Vleck Chair Professor at University of Wisconsin-Madison (1996-2005) and a Bill Fulton Collegiate Chair Professor at University of Michigan (1996-2020). He was an invited speaker for ICM98, a Sloan Research Fellow and an AMS fellow.

Professor Liu Yifeng has online published a research paper by Annals of Mathematics

Chow groups and LL-derivatives of automorphic motives for unitary groupsPages 817-901 from Volume 194 (2021), Issue 3 by Chao Li, Yifeng LiuAbstractIn this article, we study the Chow group of the motive associated to a tempered global LL-packet ππ of unitary groups of even rank with respect to a CM extension, whose global root number is −1−1. We show that, under some restrictions on the ramification of ππ, if the central derivative L′(1/2,π)L′(1/2,π) is nonvanishing, then the ππ-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson–Bloch conjecture for Chow groups and LL-functions, which generalizes the Birch and Swinnerton-Dyer conjecture. Moreover, assuming the modularity of Kudla’s generating functions of special cycles, we explicitly construct elements in a certain ππ-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative L′(1/2,π)L′(1/2,π) and local doubling zeta integrals. This confirms the conjectural arithmetic inner product formula proposed by one of us, which generalizes the Gross–Zagier formula to higher dimensional motives.Show/hide bibliography for this articlePublished online: 2 November 2021

Professor Liu Yifeng has online published a research paper by Annals of Mathematics

Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecturePages 519-584 from Volume 194 (2021), Issue 2 by Raphaël Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen ZhuAbstractWe introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n)×U(n+1)U(n)×U(n+1) in the stable case.Show/hide bibliography for this articlePublished online: 13 August 2021

Professor Liu Yifeng Joined IASM as the Fourth Permanent Member

Professor Liu Yifeng Joined IASM as the fourth permanent member on June 1st 2021. Yifeng was previously a C.L.E. Moore Instructor at MIT (2012-2015), an Assistant Professor at Northwestern University (2015-2018) and an Associate Professor and then a Professor at Yale University (2018-2021).Yifeng’s research focuses on Algebraic Number Theory, Automorphic Forms and Algebraic Geometry, especially in the arithmetic aspect of the Langlands program. Born in 1985, Yifeng obtained his bachelor’s degree from Peking University in 2007 and his doctorate from Columbia University in 2012. He received a Sloan Research Fellowship in 2017 and was awarded the 2018 SASTRA-Ramanujan Prize shared with Jack Thorne.

Professor Ruan Yongbin has online published a research paper by Inventiones mathematicae

The logarithmic gauged linear sigma modelInventiones mathematicae volume 225, pages1077–1154 (2021) by Qile Chen, Felix Janda & Yongbin Ruan AbstractWe introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov–Witten invariants of complete intersections.Published: 06 April 2021