ILJU Academic and Cultural Research Foundation

“ILJU Academy and Culture Foundation” was found on July 19, 1990 by Mr. Im-Yong Lee (1921~1996), also known as ILJU, the founder of Taekwang Industrial Co., Ltd. Since its foundation, it has steadily provided scholarships and research fund to various educational institutions, researchers and students. ILJU Academy and Culture Foundation has spent over KRW 30.2 billion so far, and also manages ILJU & SEONHWA Gallery and Media Archive to support development of art and culture in Korea.

ILJU School of Mathematics

The aim of ILJU  School of Mathematics to intoroduce recent research problems on mathematics  including basic material so that graduate students and post-doctoral fellows are encouraged to solve them and also to increase communication and friendship between participants.

Modular forms and automorphic representations are not only interesting subjects on their own right but also powerful analytic tools for investigating subtle arithmetic properties of Galois groups and algebraic varieties. This principle can be turned on its head, allowing us to apply arithmetic tools to gain insight into the existence and nature of associated modular forms (and more generally automorphic representations). Well known examples are Deligne's proof of the Ramanujan conjecture, Wiles' proof of the Shimura-Taniyama conjecture (from which Fermat's Last Theorem was derived) and the recent proof of Serre conjecture due to Khare and Wintenberger. One of the most fascinating bridges between arithmetic and analytic worlds is the conjectural Langlands correspondence. It has the nice feature to match the L-functions on both sides, perhaps the most important invariants of all. Though the Langlands correspondence has been only partially established to this day, its known instances play a crucial role in the above examples.

In this 2^nd ILJU School of Mathematics we would like to provide a comprehensive introduction to the beautiful ideas circling around the interaction between modular forms, algebraic varieties and the representations of Galois groups. More specifically our focus will be congruences between modular forms as well as their arithmetic counterparts. The aim is to help participants digest some of the fundamental theories (first week) and to expose them to some of the most exciting developments in the late 20th century (second week) so that they are motivated enough to pursue these subjects further.

Place

Mathematical Science Bldg, Room 402, POSTECH
-Only on July 29 will be held in Posco International Center 2F(Conference room C,D)-

POSTER