- Speaker : Keunyoung Jeong (UNIST)
- Title : Rational points on curves and Birch-Swinnerton-Dyer conjecture
* Time : April 21 (Wed.) 16:00-18:00
* Zoom ID : 864 5114 2655
(Zoom link : https://unist-kr.zoom.us/j/86451142655)
* Abstract : In the first half of this introductory talk, we review basic concepts of Diophantine geometry including elliptic curves, hyperelliptic curves their L-functions, and Birch-Swinnerton-Dyer conjecture. Also, we introduce some known results on BSD conjecture and arithmetic statistics.
After that, we explain how to give a bound on the number of rational points on elliptic curves and hyperelliptic curves. Based on this technique, we talk about problems of constructing abelian varieties with given algebraic/analytic rank, which sometimes make an example satisfying BSD conjecture.