The 62nd KMGS will be held on October 8, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Seunghoon Jeong from the Dept. of Mathematics, POSTECH.
The abstract of the talk is as follows.
[Speaker] 정승훈 (Seunghoon Jeong) from Dept. of Mathematics, POSTECH, supervised by Prof. 최범준, Beomjun Choi
[Title] Łojasiewicz Theory on the Wasserstein Space
[Discipline] Analysis
[Abstract]
Over the past two decades, gradient flows in the optimal transport framework have found wide-ranging applications in PDEs, probability, and machine learning. However, the long-time behavior of Wasserstein gradient flows for genuinely nonconvex energies remains much less understood.In geometric analysis, Łojasiewicz-type inequalities provide a powerful framework for studying the asymptotic behavior of gradient flows near critical points. This theory, originating from Łojasiewicz’s work in the 1960s and Simon’s infinite-dimensional extension in 1983, also encompasses questions such as Thom’s gradient conjecture on the asymptotic direction of analytic gradient trajectories.In this talk, I will discuss a Łojasiewicz theory for nonconvex Wasserstein gradient flows. As applications, we study the long-time behavior of the Keller–Segel equation for chemotactic aggregation and simplified mean-field models of self-attention dynamics motivated by in-context learning. This is joint work in progress with Beomjun Choi (KAIST), Pei-Ken Hung (University of Illinois Urbana-Champaign), and Geuntaek Seo (POSTECH).
[Language] Korean but English if it is requested