Title: The Box-Ball System from a Probabilistic Perspective

Speaker: Minjun Kim (POSTECH Mathematics)

Abstract: The box-ball system (BBS) is an ultradiscretization of the Korteweg–De Vries (KdV) equation, which describes the evolution of waves in shallow water. A key feature of the BBS is that its configurations decompose into solitons that are conserved over time. Such solitonic behavior has also attracted considerable interest from a probabilistic perspective, leading to many studies on probabilistic aspects of the BBS. In this talk, I will review several probabilistic results on the BBS and discuss some of my recent and ongoing work.

Title: Langlands program and Arthur's Trace formula

Speaker: Yuchan Lee (POSTECH Mathematics)

Abstract: The Langlands program is a far-reaching network of conjectures connecting number theory, representation theory, and algebraic geometry. It predicts deep relationships between Galois representations and automorphic forms, unifying various reciprocity laws. In this talk, I will introduce the Langlands program through its selected historical developments, starting from Langlands' letter in 1967 to Weil. I will then discuss Langlands functoriality based on the trace formula, and conclude with an overview of my work and ongoing projects