Monday, March 23, 2026

2026-03-25 / 22:00 ~ 23:00

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We consider the computation of internal solutions for a time domain plasma wave equation with unknown coefficients from the data obtained by sampling its transfer function at the boundary. The computation is performed by transforming the background snapshots for a known background coefficient using the Cholesky decomposition of the data-driven Gramian. We show that this approximation is asymptotically close to the projection of the internal solution onto the subspace of background snapshots. This allows us to derive a generally applicable bound for the error in the approximation of internal fields from boundary data only for a time domain plasma wave equation with an unknown potential q. We use this to show convergence for general unknown $q$ in one dimension. We show numerical experiments and applications to SAR imaging in higher dimensions.

2026-03-25 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 콜로퀴엄: 복잡한 생화학 반응 네트워크의 확률 이론

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Biochemical reaction networks and gene regulatory networks in cells are prototypical examples of complex systems, characterized by highly nonlinear and stochastic, multilevel dynamical interactions. Gaining a deep understanding of the stochastic dynamics and thermodynamic principles governing biochemical reaction networks not only helps elucidate the intrinsic mechanisms underlying cell fate decisions and the onset and progression of diseases, but also provides new theoretical paradigms for the study of complex systems. This line of research has become one of the forefront interdisciplinary areas, bridging mathematics, physics, biology, chemistry, statistics, and intelligent science. In this talk, I will present our recent research progress in this area, with the hope of stimulating further discussion and inspiring new ideas.

2026-03-26 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나:

by 이현우(카이스트 수리과학과 & IBS ECOPRO)

The celebrated formula of Otter \emph{[Ann. of Math. (2) 49 (1948), 583--599]} asserts that the complete graph contains exponentially many non-isomorphic spanning trees. In this paper, we show that every connected almost regular graph with sufficiently large degree already contains exponentially many non-isomorphic spanning trees. Indeed, we prove a stronger statement: for every fixed $n$-vertex tree $T$, $$\Pr\bigl[\mathcal{T} \simeq_{\mathrm{iso}} T\bigr] = e^{-\Omega(n)},$$ where $\mathcal{T}$ is a uniformly random spanning tree of a connected $n$-vertex almost regular graph with sufficiently large degree. To prove this, we introduce a graph-theoretic variant of the classical balls--into--bins model, which may be of independent interest.

2026-03-30 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식:

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We establish the stability of a pair of Hill's spherical vortices moving away from each other in 3D incompressible axisymmetric Euler equations without swirl. Each vortex in the pair propagates away from its odd-symmetric counterpart, while keeping its vortex profile close to Hill's vortex. This is achieved by analyzing the evolution of the interaction energy of the pair and combining it with the compactness of energy-maximizing sequences in the variational problem concerning Hill's vortex. The key strategy is to confirm that, if the interaction energy is initially small enough, the kinetic energy of each vortex in the pair remains so close to that of a single Hill's vortex for all time that each vortex profile stays close to the energy maximizer: Hill's vortex. An estimate of the propagating speed of each vortex in the pair is also obtained by tracking the center of mass of each vortex. This estimate is optimal in the sense that the power exponent of the epsilon (the small perturbation measured in the "L^1+L^2+impulse" norm) appearing in the error bound cannot be improved. This talk is based on the paper [Y.-J. Sim, Nonlinearity, 2026].

2026-03-24 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Characterizing large clique number in tournaments

by Hidde Koerts(University of Waterloo)

A backedge graph of a tournament $T$ with respect to a total ordering $\prec$ of the vertices of $T$ is a graph on $V(T)$ where $uv$ is an edge if and only if $uv \in A(T)$ and $v \prec u$. In 2023, Aboulker, Aubian, Charbit and Lopes introduced the clique number of tournaments based on backedge graphs as a natural counterpart to the dichromatic number of tournaments. Specifically, the clique number of a tournament is the minimum clique number of a backedge graph when considering all possible orderings. Given this definition, it is not immediately clear what the canonical clique object should be. In this talk, we provide an answer to this question. We show that if a tournament has large clique number, it contains a reasonably large subtournament from one of two simple and previously studied families of tournaments of unbounded clique number. This talk is based on joint work with Logan Crew, Xinyue Fan, Benjamin Moore, and Sophie Spirkl.

2026-03-23 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식:

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We discuss sharp local smoothing estimates for curve averages. The proof introduces a new method for estimating oscillatory integrals based on wave packet analysis and a high–low decomposition. We outline the main ideas of the local smoothing estimates for curve averages in three dimensions, focusing on the treatment of the relevant oscillatory integrals.

Events for the 취소된 행사 포함