Monday, September 8, 2025

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2025-09-09 / 09:00 ~ 10:00
학과 세미나/콜로퀴엄 - 박사논문심사: 인쇄
by 백주헌(카이스트 수리과학과)

2025-09-09 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: 인쇄
by ()
Stochastic Volterra equations (SVEs for short) are useful to model dynamics with hereditary properties, memory effects and roughness of the path, which cannot be described by standard SDEs. However, the analysis of SVEs is much more difficult than the SDEs case since the solutions are no longer Markovian or semimartingales in general. In this talk, we introduce an infinite dimensional framework which captures Markov and semimartingale structures behind SVEs. We show that an SVE can be “lifted” to an infinite dimensional stochastic evolution equation (SEE for short) and that the solution of the SEE becomes a Markov process on a Hilbert space. Furthermore, we establish asymptotic properties and well-posedness results for lifted SEEs, and then apply them to the original SVEs.
2025-09-11 / 11:50 ~ 12:40
대학원생 세미나 - 대학원생 세미나: Toward an induced grid minor theorem 인쇄
by 최무진(KAIST & IBS DIMAG)
The Grid Minor Theorem by Robertson and Seymour is one of the most important results in structural graph theory. In recent years, there has been growing interest in exploring an induced analogue of this theorem. In this talk, we prove that for all positive integers $k$ and $d$, the class of $K_{1,d}$-free graphs not containing the $k$-ladder or the $k$-wheel as an induced minor has a bounded tree-independence number. These two graphs can be considered as strong evidence for existence of a grid as an induced minor. Our proof uses a generalization of the concept of brambles for tree-independence number. This is based on joint work with Claire Hilaire, Martin Milanič, and Sebastian Wiederrecht.
2025-09-15 / 16:00 ~ 17:30
편미분방정식 통합연구실 세미나 - 편미분방정식: 인쇄
by 최범준()

2025-09-09 / 16:00 ~ 17:00
SAARC 세미나 - 콜로퀴엄: 인쇄
by ()
Stochastic Volterra equations (SVEs for short) are useful to model dynamics with hereditary properties, memory effects and roughness of the path, which cannot be described by standard SDEs. However, the analysis of SVEs is much more difficult than the SDEs case since the solutions are no longer Markovian or semimartingales in general. In this talk, we introduce an infinite dimensional framework which captures Markov and semimartingale structures behind SVEs. We show that an SVE can be “lifted” to an infinite dimensional stochastic evolution equation (SEE for short) and that the solution of the SEE becomes a Markov process on a Hilbert space. Furthermore, we establish asymptotic properties and well-posedness results for lifted SEEs, and then apply them to the original SVEs.
2025-09-11 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by 이성빈(카이스트 물리학과)
In quantum many-body systems, complexity arises not from randomness alone, but from the rich interplay of interactions and entanglement. These systems often exhibit emergent behavior, where global coherence emerges in ways that are absent in single- or few-body descriptions. While most many-body systems are governed by short-range interactions, we explore how strong correlations can arise even between spatially distant degrees of freedom by introducing the concept of multifractality in wave functions. In this talk, we present new perspectives on how quantum many-body systems can exhibit long-range and effectively all-to-all coupling, despite being governed by local Hamiltonians. We highlight key examples where multifractal wave functions naturally appear, such as in quasiperiodic systems, systems with mobility edges, and near localization–delocalization transitions. These critical states possess spatially inhomogeneous amplitude distributions that mediate strong, non-local entanglement and random long-distance couplings, offering a novel route toward engineering globally connected quantum systems.
2025-09-09 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Symmetry breaking in trees 인쇄
by Katherine Perry(Soka University of America)
We will discuss two symmetry breaking parameters: distinguishing number and fixing number. Despite being introduced independently, they share meaningful connections. In particular, we show that if a tree is 2-distinguishable with order at least 3, it suffices to fix at most 4/11 of the vertices and if a tree is $d$-distinguishable, $d \geq 3$, it suffices to fix at most $\frac{d-1}{d+1}$ of the vertices. We also characterize the $d$-distinguishable trees with radius $r$, for any $d \geq 2$ and $r \geq 1$. This is joint work with Calum Buchanan, Peter Dankleman, Isabel Harris, Paul Horn, and Emily Rivett-Carnac.
2025-09-08 / 16:00 ~ 17:30
편미분방정식 통합연구실 세미나 - 편미분방정식: Strichartz estimates for the linear Schrödinger equation 인쇄
by 곽범종()
We consider a class of linear estimates for evolution PDEs on the Euclidean space, called Strichartz estimate. Strichartz estimates are well-established for fundamental linear PDEs, such as heat and wave equations. As a simple model of such, we consider the Schrödinger example, introducing classical Strichartz estimates with proofs. Reference Terence Tao, Nonlinear dispersive equations: local and global analysis, Chapter 2.3
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