Abstract: 

Birch and Swinnerton-Dyer conjecture is one of the most famous and important problem in pure math, which predicts deep relations between several invariants of elliptic curves defined over number fields. In 1980s, Beilinson, Bloch, and Kato proposed a vast generalization of this conjecture to motives over number fields. In this talk, we will survey results in recent years concerning Beilinson-Bloch-Kato conjectures, and explain major ingredients in their proofs.

Bio:

Yifeng Liu joined the IASM (Institute for Advanced Study in Mathematics at Zhejiang University) as a permanent member in June 2021. He obtained his bachelor's degree from Peking University in 2007 and his doctorate from Columbia University in 2012. He was a C.L.E. Moore Instructor at MIT (2012—2015), an Assistant Professor at Northwestern University (2015—2018), an Associate Professor and then a Professor at Yale University (2018—2021) right before joining the IASM.

Yifeng's research areas include Algebraic Number Theory, Automorphic Forms, and Algebraic Geometry, especially in the arithmetic aspect of the Langlands program. He received a Sloan Research Fellowship in 2017 and was awarded the 2018 SASTRA-Ramanujan Prize shared with Jack Thorne.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=BSD_in_higher_dimensions.html