Thursday, May 15, 2025

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2025-05-22 / 11:50 ~ 12:40
대학원생 세미나 - 대학원생 세미나: 인쇄
by 이아로(카이스트 수리과학과)
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).
2025-05-16 / 10:00 ~ 11:00
학과 세미나/콜로퀴엄 - 박사논문심사: Time-asymptotic behavior toward viscous shocks for Compressible Navier-Stokes equations 인쇄
by 이호빈()

2025-05-16 / 09:00 ~ 10:00
학과 세미나/콜로퀴엄 - 박사논문심사: 1차원 압축성 Navier–Stokes–Korteweg 방정식에서 점성–분산 충격파 및 복합파의 시간 점근적 안정성 인쇄
by 한성호(KAIST)

2025-05-21 / 10:00 ~ 11:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
If M is a hyperbolic 3-manifold fibering over the circle, then the fundamental group of M acts faithfully by homeomorphisms on a circle—the circle at infinity of the universal cover of the fiber—preserving a pair of invariant (stable and unstable) laminations. Many different kinds of dynamical structures including taut foliations and quasigeodesic or pseudo-Anosov flows are known to give rise to universal circles—a circle with a faithful action of the fundamental group preserving a pair of invariant laminations—and those universal circles play a key role in relating the dynamical structure to the geometry of M. In my minicourse and in my colloquium talk, I will introduce the idea of *zippers*, which give a new and direct way to construct universal circles, streamlining the known constructions in many cases, and giving a host of new constructions in others. In particular, zippers—and their associated universal circles—may be constructed directly from homological objects (uniform quasimorphisms), causal structures (uniform left orders), and many other structures.
2025-05-20 / 10:00 ~ 11:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
If M is a hyperbolic 3-manifold fibering over the circle, then the fundamental group of M acts faithfully by homeomorphisms on a circle—the circle at infinity of the universal cover of the fiber—preserving a pair of invariant (stable and unstable) laminations. Many different kinds of dynamical structures including taut foliations and quasigeodesic or pseudo-Anosov flows are known to give rise to universal circles—a circle with a faithful action of the fundamental group preserving a pair of invariant laminations—and those universal circles play a key role in relating the dynamical structure to the geometry of M. In my minicourse and in my colloquium talk, I will introduce the idea of *zippers*, which give a new and direct way to construct universal circles, streamlining the known constructions in many cases, and giving a host of new constructions in others. In particular, zippers—and their associated universal circles—may be constructed directly from homological objects (uniform quasimorphisms), causal structures (uniform left orders), and many other structures.
2025-05-19 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
If M is a hyperbolic 3-manifold fibering over the circle, then the fundamental group of M acts faithfully by homeomorphisms on a circle—the circle at infinity of the universal cover of the fiber—preserving a pair of invariant (stable and unstable) laminations. Many different kinds of dynamical structures including taut foliations and quasigeodesic or pseudo-Anosov flows are known to give rise to universal circles—a circle with a faithful action of the fundamental group preserving a pair of invariant laminations—and those universal circles play a key role in relating the dynamical structure to the geometry of M. In my minicourse and in my colloquium talk, I will introduce the idea of *zippers*, which give a new and direct way to construct universal circles, streamlining the known constructions in many cases, and giving a host of new constructions in others. In particular, zippers—and their associated universal circles—may be constructed directly from homological objects (uniform quasimorphisms), causal structures (uniform left orders), and many other structures.
2025-05-15 / 14:30 ~ 15:30
학과 세미나/콜로퀴엄 - 정수론: 인쇄
by 선해상(울산과학기술)
I will discuss how to study the mod p non-vanishing problem for Dirichlet L-values with characters whose kernels are unbounded as the conductors grow. Main ingredients are a dynamical reformulation of the problem using a variant of trace defined by Poisson kernel and a study on the spectral properties of transfer operators related to p-Bernoulli map on the interval. This is ongoing research joint with A. Burungale.
2025-05-16 / 14:00 ~ 15:30
학과 세미나/콜로퀴엄 - 기타: Introduction to Homotopical Algebra through Model Categories II 인쇄
by Naing Zaw Lu(KAIST)
(This is part of the reading seminar given by the undergrad student Mr. Naing Zaw Lu for his Individual Study project.) This is an introductory talk on homotopy theory in model categories. Over the course of three lectures, we will familiarize ourselves with model categories, see how powerful cofibrant/fibrant objects can be, and build up the tools necessary to define the (Quillen) homotopy category of a model category.
2025-05-20 / 16:00 ~ 17:00
학과 세미나/콜로퀴엄 - 박사논문심사: 칼로제로-모저 미분 비선형 슈뢰딩거 방정식에 대한 폭발 역학에 대하여 인쇄
by 김태규()

2025-05-15 / 15:00 ~ 16:00
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
A knot bounds an oriented compact connected surface in the 3-sphere, and consequently in the 4-ball. The 4-genus of a knot is the minimal genus among all such surfaces in the 4-ball, and the 4-genus of a link is defined analogously. In this talk, I will discuss lower bounds on the 4-genus derived from Cheeger-Gromov-von Neumann rho-invariants. This is joint work with Jae Choon Cha and Min Hoon Kim.
2025-05-20 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: 인쇄
by 윤상두()
In this talk, we will discuss the current state and future prospects of multimodal AI. In particular, we will focus on the key challenges in ensuring reliability and efficiency in multimodal AI, explaining why addressing these factors is crucial for the successful real-world deployment of next-generation intelligent systems.
2025-05-19 / 16:00 ~ 17:30
편미분방정식 통합연구실 세미나 - 편미분방정식: Existence and uniqueness of global strong solutions for one-dimensional compressible navier-stokes equations 인쇄
by 은남현()
Abstract: In this talk, we discuss the global-in-time existence of strong solutions to the one-dimensional compressible Navier-Stokes system. Classical results establish only local-in-time existence under the assumption that the initial data are smooth and the initial density remains uniformly positive. These results can be extended to global-in-time existence using the relative entropy and Bresch-Desjardins entropy under the same hypotheses. This approach allows for possibly different end states and degenerate viscosity. Reference: A. Mellet and A. Vasseur, Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. SIAM J. Math. Anal., 39(4):1344–1365, 2007/08.
2025-05-22 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
TBD
2025-05-15 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by 선해상(UNIST 수리과학과)
Arithmetic of Elliptic curves, one of fundamental research themes in modern number theory, is encoded in the special values of elliptic L-functions. For example, Mazur-Rubin heuristics on the distribution of the special L-values predict the behavior of ranks of elliptic curves. The average version of the heuristics was proved by several researchers including myself several years ago. In the talk, I will present how to use the dynamics of continued fractions to study the problem and introduce an approach to study the original problem, i.e., non-average version, after introducing a classical result, so-called Lochs' theorem, which compares entropies of two distinct dynamical systems.
2025-05-21 / 16:00 ~ 17:00
IBS-KAIST 세미나 - IBS-KAIST 세미나: 인쇄
by ()
Many natural systems exhibit oscillations that show sizeable fluctuations in frequency and amplitude. This variability can arise from a wide variety of physical mechanisms. Phase descriptions that work for deterministic oscillators have a limited applicability for stochastic oscillators. In my talk I review attempts to generalize the phase concept to stochastic oscillations, specifically, the mean-return-time phase and the asymptotic phase. For stochastic systems described by Fokker-Planck and Kolmogorov-backward equations, I introduce a mapping of the system’s variables to a complex pointer (instead of a real-valued phase) that is based on the eigenfunction of the Kolmogorov equation. Under the new (complex-valued) description, the statistics of the oscillator’s spontaneous activity, of its response to external perturbations, and of the coordinated activity of (weakly) coupled oscillators, is brought into a universal and greatly simplified form. The theory is tested for three theoretical models of noisy oscillators arising from fundamentally different mechanisms: a damped harmonic oscillator with dynamical noise, a fluctuation-perturbed limit-cycle system, and an excitable system in which oscillations require noise to occur.
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