Tuesday, April 15, 2025

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2025-04-15 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: A Minor Characterisation of Normally Spanned Sets of Vertices 인쇄
by Nicola Lorenz(University of Hamburg)
A rooted spanning tree of a graph $G$ is called normal if the endvertices of all edges of $G$ are comparable in the tree order. It is well known that every finite connected graph has a normal spanning tree (also known as depth-first search tree). Also, all countable graphs have normal spanning trees, but uncountable complete graphs for example do not. In 2021, Pitz proved the following characterisation for graphs with normal spanning trees, which had been conjectured by Halin: A connected graph $G$ has a normal spanning tree if and only if every minor of $G$ has countable colouring number, i.e. there is a well-order of the vertices such that every vertex is preceded by only finitely many of its neighbours. More generally, a not necessarily spanning tree in $G$ is called normal if for every path $P$ in $G$ with both endvertices in $T$ but no inner vertices in $T$, the endvertices of $P$ are comparable in the tree order. We establish a local version of Pitz’s theorem by characterising for which sets $U$ of vertices of $G$ there is a normal tree in $G$ covering $U$. The results are joint work with Max Pitz.
2025-04-16 / 16:00 ~ 18:00
학과 세미나/콜로퀴엄 - 위상수학 세미나: 인쇄
by ()
The Lipshitz-Ozsvath-Thurston correspondence is a combinatorial way to describe the bordered Floer homology of a knot complement from the UV=0 coefficient knot Floer homology of the given knot. This is then used to compute the knot Floer homology of satellite knots. In this talk, we show that there is a "relative" version of this correspondence, between homotopy classes of type D morphisms of bordered Floer homology and locally symmetric chain maps of knot Floer complexes, modulo the "canonical negative class". This gives us a fully combinatorial process to compute knot Floer cobordism maps of satellite concordances in the UV=0 knot Floer homology.
2025-04-22 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Burling Graphs as (almost) universal obstacles to $\chi$-boundedness 인쇄
by Marcin Briański(Jagiellonian University)
What causes a graph to have high chromatic number? One obvious reason is containing a large clique (a set of pairwise adjacent vertices). This naturally leads to investigation of \(\chi\)-bounded classes of graphs — classes where a large clique is essentially the only reason for large chromatic number. Unfortunately, many interesting graph classes are not \(\chi\)-bounded. An eerily common obstruction to being \(\chi\)-bounded are the Burling graphs — a family of triangle-free graphs with unbounded chromatic number. These graphs have served as counterexamples in many settings: demonstrating that graphs excluding an induced subdivision of \(K_{5}\) are not \(\chi\)-bounded, that string graphs are not \(\chi\)-bounded, that intersection graphs of boxes in \({\mathbb{R}}^{3}\) are not \(\chi\)-bounded, and many others. In many of these cases, this sequence is the only known obstruction to \(\chi\)-boundedness. This led Chudnovsky, Scott, and Seymour to conjecture that any graph of sufficiently high chromatic number must either contain a large clique, an induced proper subdivision of a clique, or a large Burling graph as an induced subgraph. The prevailing belief was that this conjecture should be false. Somewhat surprisingly, we did manage to prove it under an extra assumption on the “locality” of the chromatic number — that the input graph belongs to a \(2\)-controlled family of graphs, where a high chromatic number is always certified by a ball of radius \(2\) with large chromatic number. In this talk, I will present this result and discuss its implications in structural graph theory, and algorithmic implications to colouring problems in specific graph families. This talk is based on joint work with Tara Abrishami, James Davies, Xiying Du, Jana Masaříková, Paweł Rzążewski, and Bartosz Walczak conducted during the STWOR2 workshop in Chęciny Poland.
2025-04-21 / 16:00 ~ 17:00
편미분방정식 통합연구실 세미나 - 편미분방정식: The dispersion-managed nonlinear Schrödinger equation with power-type nonlinearity 인쇄
by 이영란()
In this talk, we consider the dispersion-managed nonlinear Schrödinger equation (DM NLS), which naturally arises in modeling of fiber-optic communication systems with periodically varying dispersion profiles. We discuss the well-posedness of the DM NLS and the threshold phenomenon related to the existence of minimizers for its ground states.
2025-04-18 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by 송윤민()
In this talk, we discuss the paper “Identifying key drivers in a stochastic dynamical system through estimation of transfer entropy between univariate and multivariate time series” by Julian Lee, Physical Review E, 2025.
2025-04-22 / 16:00 ~ 17:00
SAARC 세미나 - SAARC 세미나: 인쇄
by 김선우(연세대학교 수학과)
The talk is divided into two parts. In the first part, we review the concept of phase transition in probability theory and mathematical physics, focusing on the standard +/- Ising model. In the second part, we discover why one may expect metastability in the low-temperature regime, and look at some concrete examples that exhibit this phenomenon.
Events for the 취소된 행사 포함 모두인쇄
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