In this talk I shall describe how the components of J_b-orbits of an affine Deligne-Lusztig varieties contribute to the components of the basic locus of a Shimura variety. Then we shall present results for the cases of PEL-type A and C and describe the mass formula part for type C. This is based on joint works with Jiangwei Xue and Yasuhiro Terakado.
One of the main topics in Random Matrix Theory(RMT) is universality. In this talk, we focus on edge universality in Wigner matrices. With overall description of significant findings including spiked Wigner matrix and BBP transition, we introduce our recent topic, fluctuations of the largest eigenvalues of transformed spiked Wigner matrices. We provide precise formulas for the limiting distributions and also concentration estimates for the largest eigenvalues, both in the supercritical and the subcritical regimes. This is a joint work with Prof. Ji Oon Lee (KAIST).
2025-05-27 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Counterexample to Babai’s lonely colour conjecture
by Meike Hatzel(IBS 이산수학 그룹)
Motivated by colouring minimal Cayley graphs, in 1978 Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by constructing graphs of arbitrarily large girth and chromatic number that have a proper edge colouring in which each cycle contains no colour exactly once.
The result presented is the joint work with James Davies and Liana Yepremyan.
학과 세미나/콜로퀴엄 - 기타: Grothendieck groups of regular schemes 3
by 우태윤(KAIST)
This is a reading seminar presented by the graduate student, Mr. Taeyoon Woo. Following the lecture note of Yuri Manin, he will study K_0 of schemes, and its essential properties, such as functoriality, projective bundle formula, filtrations, relationship to Picard group, blow-up squares, Chern classes, Todd classes and the Grothendieck-Riemann-Roch theorem.
This talk concerns the classification problem of long-term dynamics for critical evolutionary PDEs. I will first discuss critical PDEs and soliton resolution for these equations. Building upon soliton resolution, I will further introduce the classification problem. Finally, I will also touch on a potential instability mechanism of finite-time singularities for some critical PDEs, suggesting the global existence of generic solutions.
2025-05-26 / 16:00 ~ 17:30
편미분방정식 통합연구실 세미나 - 편미분방정식: Regularity of solutions of shock reflection by large-angle wedges for potential flow
by 강수민()
Abstract :
When a plane shock hits a wedge head on, it experiences a reflection diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. In particular, the C^{1,1}-regularity is optimal for the solution across the pseudo-sonic circle and at the point where the pseudo-sonic circle meets the reflected shock where the wedge has large-angle. Also, one can obtain the C^{2,\alpha} regularity of the solution up to the pseudo-sonic circle in the pseudo-subsonic region.
Reference :
Myoungjean Bae, Gui-Qiang Chen, and Mikhail Feldman. "Regularity of solutions to regular shock reflection for potential flow." (2008)
Gui-Qiang Chen and Mikhail Feldman. "Global Solutions of Shock Reflection by Large-Angle Wedges for Potential Flow"
