Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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Special Colloquium - Congling Qiu (MIT)

Event Type

Seminar/Symposium

Sponsor

Department of Mathematics

Location

1092 Lincoln Hall

Date

Dec 7, 2023 11:30 am

Contact

Scott Ahlgren

E-Mail

sahlgren@illinois.edu

Views

243

Originating Calendar

Mathematics Colloquium & Named Lectures

Modified diagonal and symmetry of a curve

The modified diagonal on the triple product of a curve was first introduced by Gross and Schoen in the 90s. This simply defined object holds fundamental importance in the study of the geometry and arithmetic of curves. One basic question is whether the modified diagonal vanishes under “deformation.” I will introduce the origin of this type of question and provide a brief history of the study of the modified diagonal. Subsequently, I will discuss my collaborative works with W. Zhang, where we demonstrated that such vanishing can be dictated by the symmetry of the curve. As an application in number theory, we proved a case of the notorious Beilinson—Bloch conjecture, a generalization of the Millennium Birch—Swinnerton-Dyer conjecture. Finally, I will propose some new questions.

Zoom Details
Link: https://illinois.zoom.us/j/87090781306?pwd=QmRic3I3aHhPbmFwbk5sMUhFeWRoUT09

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