Diophantine problems and p-adic period mappings
In 1980s, Faltings proved the Mordell conjecture which states that any smooth projective curve over a number field of genus greater than 1 has only finitely many rational points. In this course, we will go over a different proof recently given by Lawrence and Venkatesh using p-adic Hodge theory; they consider a p-adic period map which encodes the variation of p-adic Galois representations in a family of algebraic varieties, and study its relation to the complex period map. We will also discuss their application of the method to higher dimensional situations.
Lecturer
Date
19th March ~ 18th June, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 10:00 - 11:35 | A3-1a-204 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Basic algebraic geometry and algebraic number theory
Syllabus
TBA
Reference
"Diophantine problems and p-adic period mappings" by Lawrence and Venkatesh, Invent. Math. (2020)
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
Yes
Language
English
Lecturer Intro
Yong Suk Moon joined BIMSA in 2022 fall as an assistant professor. His research area is number theory and arithmetic geometry. More specifically, his current research focuses on p-adic Hodge theory, Fontaine-Mazur conjecture, and p-adic Langlands program. He completed his Ph.D at Harvard University in 2016, and was a Golomb visiting assistant professor at Purdue University (2016-19) and a postdoctoral researcher at University of Arizona (2019 - 22).