Elliptic curves and the special values of L-functions

The arithmetic of special values of L-functions continues to reveal mysterious facets. The celebrated Birch and Swinnerton-Dyer (BSD) conjecture connects the structure of the set of rational points on an elliptic curve to the associated Hasse-Weil L-function. The Bloch-Kato conjecture is a vast generalization, encompassing geometric Galois representation. Over the last decade, the BSD conjecture and the Bloch-Kato conjecture have witnessed notable progress. The Gan-Gross-Prasad conjecture and variants have undergone striking advances as well. Following the online precursor last year, the program aims to report on some of these recent and emerging developments. An introduction to the recent progress towards the Brumer-Stark conjecture will also appear.