Introduction to Beilinson--Kato elements and their applications 1 by Chan-Ho Kim

PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE)

ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China)

DATE : 02 August 2021 to 07 August 2021
VENUE : Online
Understanding the structure of the set of rational points on an elliptic curve - essentially a cubic equation - has been an aim in number theory for over a century. It has connections to open problems buried in antiquity, such as the congruent number problem. The Birch and Swinnerton-Dyer (BSD) conjecture, a Clay millennium problem, predicts a mystifying interrelation among the rational points and the associated L-function. The Bloch-Kato conjecture is a vast generalisation of the BSD conjecture. Over the last decade, the BSD has witnessed notable progress.

In this precursor to the upcoming program on the recent progress, a series of mini-courses is intended mainly as an introduction to some of the breakthroughs towards the BSD conjecture from the mid 1970's - the early 1990's; namely after: Coates-Wiles, Gross-Zagier and Kolyvagin, Kato. An introduction to recent progress towards the Gross-Stark conjecture will also appear.

List of speakers and mini courses for the online precursor:

Heegner Points: Francesc Castella (University of California, Santa Barbara)
Galois Representations: Shaunak Deo (IISc, Bengaluru)
On the Gross-Stark conjecture: Mahesh Kakde (IISc, Bengaluru)
Beilinson-Kato elements: Chan-Ho Kim (Korea Institute of Advanced Studies, Seoul)
Elliptic curves and Selmer groups: Anupam Saikia (IIT Guwahati) & Sudhanshu Shekhar (IIT Kanpur)
Eligibility Criteria:

Interested faculty are encouraged to register.
Any masters (MS/MSc etc.), PhD student in Mathematics, final year bachelors (BS/BSc/BTech etc.) students with a major in Mathematics are encouraged to apply. Postdoctoral researchers in mathematics can also apply.