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: 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/junior and senior faculty/other researchers in mathematics with a PhD can also apply.