
Professor Liu Yifeng has online published a research paper by Inventiones mathematicae
A padic arithmetic inner product formulaInventiones mathematicae volume 236, pages 219–3751 (2024) by Daniel Disegni & Yifeng LiuAbstractFix a prime number p and let E/F be a CM extension of number fields in which p splits relatively. Let π be an automorphic representation of a quasisplit unitary group of even rank with respect to E/F such that π is ordinary above p with respect to the Siegel parabolic subgroup. We construct the cyclotomic padic Lfunction of π, and a certain generating series of Selmer classes of special cycles on Shimura varieties. We show, under some conditions, that if the vanishing order of the padic Lfunction is 1, then our generating series is modular and yields explicit nonzero classes (called Selmer theta lifts) in the Selmer group of the Galois representation of E associated with π; in particular, the rank of this Selmer group is at least 1. In fact, we prove a precise formula relating the padic heights of Selmer theta lifts to the derivative of the padic Lfunction. In parallel to PerrinRiou’s padic analogue of the Gross–Zagier formula, our formula is the padic analogue of the arithmetic inner product formula recently established by Chao Li and the second author.Published: 23 February 2024

Professor Sun Song Joined IASM as the Fifth Permanent Member
Professor Sun Song joined IASM as the fifth permanent member in January, 2024. Professor Sun Song, Chinese, was born in February 1987 in Anqing, Anhui Province. He received his bachelor's degree from the University of Science and Technology of China (2003 2006) and his doctorate from the University of Wisconsin–Madison, USA (20062010). He had worked at Imperial College London, State University of New York at Stony Brook, and the University of California, Berkeley. Professor Sun Song's research focuses on Differential Geometry, Complex Geometry, and Geometric Analysis. He received a Sloan Research Fellowship in 2014, the Oswald Veblen Prize in Geometry in 2019, and the New Horizons in Mathematics Prize of Breakthrough Prize in 2021. He was invited to make a 45minute presentation at the International Congress of Mathematicians. Before he joined IASM, he was a professor at the University of California, Berkeley.