The KOAS Summer School brings together researchers, postdoctoral fellows, and graduate students for four days of lectures, discussions, and collaborative activities in operator algebras and related areas. The program features lecture series by leading researchers, explores current developments in the field, and provides opportunities for participants to exchange ideas, build connections, and foster future collaborations.
This summer school features lecture series by Hiroki Matui and Chris Schafhauser. Professor Matui is internationally recognized for his influential contributions to étale groupoids, topological dynamics, and the classification of operator algebras, while Professor Schafhauser has made significant advances in the classification theory of C*-algebras and related areas of noncommutative topology. Through a combination of lectures and discussion sessions, participants will have the opportunity to engage with both foundational ideas and current research directions in operator algebras.
The program also coincides with special activities of the Korean Mathematical Society, including a public lecture by Fields Medalist Martin Hairer and invited lectures in analysis
Abstract.
A conjecture of Elliott from the early 1990s predicted that unital separable simple nuclear C*-algebras are determined up to isomorphism by K-theoretic invariants. By the combined effort of many researchers over 2–3 decades, the conjecture has now been verified under two additional hypotheses: Z-stability and the Universal Coefficient Theorem (UCT). In the years following the proof of the classification conjecture, in my joint work with Carrion, Gabe, Tikuisis, and White, we provided a more conceptual proof of this result. I will discuss some aspects of the classification theory for C*-algebras, including the statement of the classification theorem, some key examples and applications, and some of the main techniques that are used.
Abstract.
The construction of C*-algebras from ample groupoids has provided a rich framework for studying the interplay between dynamics and operator algebras. A central problem in this field is the comparison between the groupoid homology and the K-theory of the associated C*-algebras. While significant progress has recently been made by Proietti and Yamashita, many fundamental questions remain open. In this talk, we focus on cases primarily related to Z^n-actions to organize the remaining open problems and report on some recent developments. Furthermore, if time permits, we shall discuss a version of the Gap-Labelling conjecture formulated in the context of ample groupoids.
Main venue for lectures and discussions.
Venue for KMS special lectures and events.
Nearby attractions:
• Lotte World Tower
• Seokchon Lake
• Han River Parks
• Gangnam
• Gyeongbokgung Palace
KOAS Summer School 2026
For inquiries regarding registration or participation, please contact the organizing committee.
email: hyun.lee7425@gmail.com, hadamard@ulsan.ac.kr