BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20210101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220907T163000
DTEND;TZID=Asia/Seoul:20220907T173000
DTSTAMP:20260417T081215
CREATED:20220614T112030Z
LAST-MODIFIED:20240705T171148Z
UID:5853-1662568200-1662571800@dimag.ibs.re.kr
SUMMARY:Dömötör Pálvölgyi\, C-P3O: Orientation of convex sets and other good covers
DESCRIPTION:We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular\, we compare it to other systems of orientations on triples that satisfy a natural interiority condition. Such systems\, P3O (partial 3-order)\, are a natural generalization of posets\, and include the order types of planar point sets. Our main result is that P3O that emerge from points sets\, p-P3O\, and P3O that emerge from convex sets\, C-P3O\, do not contain each other. We also extend our orientation to other good covers from convex sets and study the resulting P3O’s.\nBased on joint work with Agoston\, Damasdi\, and Keszegh:\nhttps://arxiv.org/abs/2206.01721\nhttps://arxiv.org/abs/2206.01723
URL:https://dimag.ibs.re.kr/event/2022-09-07/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220906T163000
DTEND;TZID=Asia/Seoul:20220906T173000
DTSTAMP:20260417T081215
CREATED:20220719T105944Z
LAST-MODIFIED:20240707T074750Z
UID:5974-1662481800-1662485400@dimag.ibs.re.kr
SUMMARY:Bjarne Schülke\, A local version of Katona's intersection theorem
DESCRIPTION:Katona’s intersection theorem states that every intersecting family $\mathcal F\subseteq[n]^{(k)}$ satisfies $\vert\partial\mathcal F\vert\geq\vert\mathcal F\vert$\, where $\partial\mathcal F=\{F\setminus x:x\in F\in\mathcal F\}$ is the shadow of $\mathcal F$.\nFrankl conjectured that for $n>2k$ and every intersecting family $\mathcal F\subseteq [n]^{(k)}$\, there is some $i\in[n]$ such that $\vert \partial \mathcal F(i)\vert\geq \vert\mathcal F(i)\vert$\, where $\mathcal F(i)=\{F\setminus i:i\in F\in\mathcal F\}$ is the link of $\mathcal F$ at $i$. \nHere\, we prove this conjecture in a very strong form for $n> \binom{k+1}{2}$. \nIn particular\, our result implies that for any $j\in[k]$\, there is a $j$-set $\{a_1\,\dots\,a_j\}\in[n]^{(j)}$ such that \[ \vert \partial \mathcal F(a_1\,\dots\,a_j)\vert\geq \vert\mathcal F(a_1\,\dots\,a_j)\vert.\]A similar statement is also obtained for cross-intersecting families.
URL:https://dimag.ibs.re.kr/event/2022-09-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220831T163000
DTEND;TZID=Asia/Seoul:20220831T173000
DTSTAMP:20260417T081215
CREATED:20220816T233139Z
LAST-MODIFIED:20240707T075512Z
UID:6033-1661963400-1661967000@dimag.ibs.re.kr
SUMMARY:Raphael Steiner\, Congruence-constrained subdivisions in digraphs
DESCRIPTION:I will present the short proof from [1] that for every digraph F and every assignment of pairs of integers $(r_e\,q_e)_{e\in A(F)}$ to its arcs\, there exists an integer $N$ such that every digraph D with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $r_e$ modulo $q_e$ for every $e \in  A(F)$. This generalizes to the directed setting the analogous result by Thomassen for undirected graphs and at the same time yields a novel proof of his result. I will also talk about how a hypergraph coloring result from [2] may help to obtain good bounds on $N$ in the special case when $F$ is subcubic. \n[1] https://arxiv.org/abs/2208.06358 \n[2] https://arxiv.org/abs/2206.13635
URL:https://dimag.ibs.re.kr/event/2022-08-31/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220830T163000
DTEND;TZID=Asia/Seoul:20220830T173000
DTSTAMP:20260417T081215
CREATED:20220830T073000Z
LAST-MODIFIED:20240707T075520Z
UID:6018-1661877000-1661880600@dimag.ibs.re.kr
SUMMARY:Jun Gao\, Number of (k-1)-cliques in k-critical graph
DESCRIPTION:We prove that for $n>k\geq 3$\, if $G$ is an $n$-vertex graph with chromatic number $k$ but any its proper subgraph has smaller chromatic number\, then $G$ contains at most $n-k+3$ copies of cliques of size $k-1$. This answers a problem of Abbott and Zhou and provides a tight bound on a conjecture of Gallai. \nThis is joint work with Jie Ma.
URL:https://dimag.ibs.re.kr/event/2022-08-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220825T100000
DTEND;TZID=Asia/Seoul:20220825T110000
DTSTAMP:20260417T081215
CREATED:20220825T010000Z
LAST-MODIFIED:20240707T075527Z
UID:6007-1661421600-1661425200@dimag.ibs.re.kr
SUMMARY:Brett Leroux\, Expansion of random 0/1 polytopes
DESCRIPTION:A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every $0/1$ polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a $0/1$ polytope in $\mathbb{R}^d$ is greater than 1 over some polynomial function of $d$. This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of a random $0/1$ polytope in $\mathbb{R}^d$ is at least $\frac{1}{12d}$ with high probability. \nAfter discussing this result and the proof\, we will mention some possible extensions. To conclude\, we will discuss some related questions about the combinatorics of random polytopes\, including the diameter problem. \nThis is joint work with Luis Rademacher.
URL:https://dimag.ibs.re.kr/event/2022-08-25/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220823T163000
DTEND;TZID=Asia/Seoul:20220823T173000
DTSTAMP:20260417T081215
CREATED:20220823T073000Z
LAST-MODIFIED:20240705T171142Z
UID:5971-1661272200-1661275800@dimag.ibs.re.kr
SUMMARY:Raul Lopes\, Temporal Menger and related problems
DESCRIPTION:A temporal graph is a graph whose edges are available only at specific times. In this scenario\, the only valid walks are the ones traversing adjacent edges respecting their availability\, i.e. sequence of adjacent edges whose appearing times are non-decreasing. \nGiven a graph G and vertices s and t of G\, Menger’s Theorem states that the maximum number of (internally) vertex disjoint s\,t-paths is equal to the minimum size of a subset X for which G-X contains no s\,t-path. This is a classical result in Graph Theory\, taught in most basic Graph Theory courses\, and it holds also when G is directed and when edge disjoint paths and edge cuts are considered instead. A direct translation of Menger’s Theorem to the temporal context has been known not to hold since an example was shown in the seminal paper by Kempe\, Kleinberg and Kumar (STOC’00). In this talk\, an overview of possible temporal versions of Menger’s Theorem will be discussed\, as well as the complexity of the related problems.
URL:https://dimag.ibs.re.kr/event/2022-08-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220816T163000
DTEND;TZID=Asia/Seoul:20220816T173000
DTSTAMP:20260417T081215
CREATED:20220718T235006Z
LAST-MODIFIED:20240705T171145Z
UID:5967-1660667400-1660671000@dimag.ibs.re.kr
SUMMARY:Noleen Köhler\, Testing first-order definable properties on bounded degree graphs
DESCRIPTION:Property testers are probabilistic algorithms aiming to solve a decision problem efficiently in the context of big-data. A property tester for a property P has to decide (with high probability correctly) whether a given input graph has property P or is far from having property P while having local access to the graph. We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree model. We show that any FO property that is defined by a formula with quantifier prefix ∃*∀* is testable\, while there exists an FO property that is expressible by a formula with quantifier prefix ∀*∃* that is not testable. In the dense graph model\, a similar picture is long known (Alon\, Fischer\, Krivelevich\, Szegedy\, Combinatorica 2000)\, despite the very different nature of the two models. In particular\, we obtain our lower bound by a first-order formula that defines a class of bounded-degree expanders\, based on zig-zag products of graphs. \nThis is joint work with Isolde Adler and Pan Peng.
URL:https://dimag.ibs.re.kr/event/2022-08-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220810T163000
DTEND;TZID=Asia/Seoul:20220810T173000
DTSTAMP:20260417T081215
CREATED:20220713T073000Z
LAST-MODIFIED:20240705T171145Z
UID:5849-1660149000-1660152600@dimag.ibs.re.kr
SUMMARY:Akash Kumar\, Random walks and Forbidden Minors
DESCRIPTION:Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk\, I will present how random walks helped make progress on algorithmic problems on planar graphs.\nIn particular\, I show how random walk based (i.e.\, spectral) approaches led to progress on finding forbidden minors [K.-Seshadhri-Stolman\, FOCS 2018] as well as on deciding planarity [K.-Seshadhri-Stolman\, STOC 2019] in bounded degree graphs within the property testing framework. I will also cover how these approaches eventually led to progress on the so-called “efficient partition oracle” problem [K.-Seshadhri-Stolman\, FOCS 2021].\nThe talk will assume minimal background by presenting a stand-alone story that should be of interest to students/researchers in computer science.
URL:https://dimag.ibs.re.kr/event/2022-08-10/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220809T163000
DTEND;TZID=Asia/Seoul:20220809T173000
DTSTAMP:20260417T081215
CREATED:20220808T073000Z
LAST-MODIFIED:20240707T075550Z
UID:5821-1660062600-1660066200@dimag.ibs.re.kr
SUMMARY:Eun Jung Kim (김은정)\, Directed flow-augmentation
DESCRIPTION:We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that\, given a directed graph G\, two integers $s\,t\in V(G)$\, and an integer $k$\, adds (randomly) to $G$ a number of arcs such that for every minimal st-cut $Z$ in $G$ of size at most $k$\, with probability $2^{−\operatorname{poly}(k)}$ the set $Z$ becomes a minimum $st$-cut in the resulting graph.\nThe directed flow-augmentation tool allows us to prove fixed-parameter tractability of a number of problems parameterized by the cardinality of the deletion set\, whose parameterized complexity status was repeatedly posed as open problems:\n(1) Chain SAT\, defined by Chitnis\, Egri\, and Marx [ESA’13\, Algorithmica’17]\,\n(2) a number of weighted variants of classic directed cut problems\, such as Weighted st-Cut\, Weighted Directed Feedback Vertex Set\, or Weighted Almost 2-SAT.\nBy proving that Chain SAT is FPT\, we confirm a conjecture of Chitnis\, Egri\, and Marx that\, for any graph H\, if the List H-Coloring problem is polynomial-time solvable\, then the corresponding vertex-deletion problem is fixed-parameter tractable. \nJoint work with Stefan Kratsch\, Marcin Pilipczuk\, Magnus Wahlström.
URL:https://dimag.ibs.re.kr/event/2022-08-09/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220803T163000
DTEND;TZID=Asia/Seoul:20220803T173000
DTSTAMP:20260417T081215
CREATED:20220720T073000Z
LAST-MODIFIED:20240707T075557Z
UID:5637-1659544200-1659547800@dimag.ibs.re.kr
SUMMARY:Lars Jaffke\, Taming graphs with no large creatures and skinny ladders
DESCRIPTION:We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a $k$-skinny-ladder as an induced minor\, then there exists a polynomial $p$ such that every $G \in \mathcal{G}$ contains at most $p(|V(G)|)$ minimal separators. By a result of Fomin\, Todinca\, and Villanger [SIAM J. Comput. 2015] the latter entails the existence of polynomial-time algorithms for Maximum Weight Independent Set\, Feedback Vertex Set and many other problems\, when restricted to an input graph from $\mathcal{G}$. Furthermore\, as shown by Gartland and Lokshtanov\, our result implies a full dichotomy of hereditary graph classes defined by a finite set of forbidden induced subgraphs into tame (admitting a polynomial bound of the number of minimal separators) and feral (containing infinitely many graphs with exponential number of minimal separators). \nJoint work with Jakub Gajarský\, Paloma T. Lima\, Jana Novotná\, Marcin Pilipczuk\, Paweł Rzążewski\, and Uéverton S. Souza.
URL:https://dimag.ibs.re.kr/event/2022-08-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220801T163000
DTEND;TZID=Asia/Seoul:20220801T173000
DTSTAMP:20260417T081215
CREATED:20220801T073000Z
LAST-MODIFIED:20240707T075606Z
UID:5867-1659371400-1659375000@dimag.ibs.re.kr
SUMMARY:Seunghun Lee (이승훈)\, Inscribable order types
DESCRIPTION:We call an order type inscribable if it is realized by a point configuration where all extreme points are all on a circle. In this talk\, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior points is inscribable\, and that the number of such order types is $\Theta(\frac{4^n}{n^{3/2}})$. We further construct an infinite family of minimally uninscribable order types. The proof of uninscribability mainly uses Möbius transformations. We also suggest open problems around inscribability. This is a joint work with Michael Gene Dobbins.
URL:https://dimag.ibs.re.kr/event/2022-08-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220727T163000
DTEND;TZID=Asia/Seoul:20220727T173000
DTSTAMP:20260417T081215
CREATED:20220727T073000Z
LAST-MODIFIED:20240705T171144Z
UID:5830-1658939400-1658943000@dimag.ibs.re.kr
SUMMARY:Noam Lifshitz\, Product free sets in the alternating group
DESCRIPTION:A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of $A_n$ be? \nIn the talk we will completely solve the problem by determining the largest product free subset of $A_n$. \nOur proof combines a representation theoretic argument due to Gowers\, with an analytic tool called hypercontractivity for global functions. We also make use of a dichotomy between structure and a pseudorandomness notion of functions over the symmetric group known as globalness. \nBased on a joint work with Peter Keevash and Dor Minzer.
URL:https://dimag.ibs.re.kr/event/2022-07-27/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220719T140000
DTEND;TZID=Asia/Seoul:20220719T160000
DTSTAMP:20260417T081215
CREATED:20220719T050000Z
LAST-MODIFIED:20240705T171145Z
UID:5880-1658239200-1658246400@dimag.ibs.re.kr
SUMMARY:Jinyoung Park (박진영)\, Thresholds 2/2
DESCRIPTION:Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006\, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set\, its threshold is never far from its “expectation-threshold\,” which is a natural (and often easy to calculate) lower bound on the threshold. \nIn the first talk on Monday\, I will introduce the Kahn-Kalai Conjecture with some motivating examples and then briefly talk about the recent resolution of the Kahn-Kalai Conjecture due to Huy Pham and myself. \nIn the second talk on Tuesday\, I will discuss our proof of the conjecture in detail.
URL:https://dimag.ibs.re.kr/event/2022-07-19/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220718T163000
DTEND;TZID=Asia/Seoul:20220718T173000
DTSTAMP:20260417T081215
CREATED:20220622T073000Z
LAST-MODIFIED:20240705T171147Z
UID:5878-1658161800-1658165400@dimag.ibs.re.kr
SUMMARY:Jinyoung Park (박진영)\, Thresholds 1/2
DESCRIPTION:Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006\, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set\, its threshold is never far from its “expectation-threshold\,” which is a natural (and often easy to calculate) lower bound on the threshold. \nIn the first talk on Monday\, I will introduce the Kahn-Kalai Conjecture with some motivating examples and then briefly talk about the recent resolution of the Kahn-Kalai Conjecture due to Huy Pham and myself. \nIn the second talk on Tuesday\, I will discuss our proof of the conjecture in detail.
URL:https://dimag.ibs.re.kr/event/2022-07-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220711T163000
DTEND;TZID=Asia/Seoul:20220711T173000
DTSTAMP:20260417T081215
CREATED:20220711T073000Z
LAST-MODIFIED:20240707T075632Z
UID:5896-1657557000-1657560600@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, Product Structure of Graph Classes with Bounded Treewidth
DESCRIPTION:The strong product $G\boxtimes H$ of graphs $G$ and $H$ is the graph on the cartesian product $V(G)\times V(H)$ such that vertices $(v\,w)$ and $(x\,y)$ are adjacent if and only if $\max\{d_G(v\,x)\,d_H(w\,y)\}=1$. Graph product structure theory aims to describe complicated graphs in terms of subgraphs of strong products of simpler graphs. This area of research was initiated by Dujmović\, Joret\, Micek\, Morin\, Ueckerdt and Wood\, who showed that every planar graph is a subgraph of the strong product of a $H\boxtimes P\boxtimes K_3$ for some path $P$ and some graph $H$ of treewidth at most $3$. In this talk\, I will discuss the product structure of various graph classes of bounded treewidth. As an example\, we show that there is a function $f:\mathbb{N}\rightarrow \mathbb{N}$ such that every planar graph of treewidth at most $k$ is a subgraph of $H\boxtimes K_{f(k)}$ for some graph $H$ of treewidth at most $3$. \nThis is based on joint work with Campbell\, Clinch\, Distel\, Gollin\, Hickingbotham\, Huynh\, Illingworth\, Tamitegama\, Tan and Wood.
URL:https://dimag.ibs.re.kr/event/2022-07-11/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220707T100000
DTEND;TZID=Asia/Seoul:20220707T110000
DTSTAMP:20260417T081215
CREATED:20220707T010000Z
LAST-MODIFIED:20240707T075642Z
UID:5783-1657188000-1657191600@dimag.ibs.re.kr
SUMMARY:Sepehr Hajebi\, Holes\, hubs and bounded treewidth
DESCRIPTION:A hole in a graph $G$ is an induced cycle of length at least four\, and for every hole $H$ in $G$\, a vertex $h\in G\setminus H$ is called a $t$-hub for $H$ if $h$ has at least $t$ neighbor in $H$. Sintiari and Trotignon were the first to construct graphs with arbitrarily large treewidth and no induced subgraph isomorphic to the “basic obstructions\,” that is\, a fixed complete graph\, a fixed complete bipartite graph (with parts of equal size)\, all subdivisions of a fixed wall and line graphs of all subdivisions of a fixed wall. They named their counterexamples “layered wheels” for a good reason: layered wheels contain wheels in abundance\, where a wheel means a hole with a $3$-hub. In accordance\, one may ask whether graphs with no wheel and no induced subgraph isomorphic to the basic obstructions have bounded treewidth. This was also disproved by a recent construction due to Davies. But holes with a $2$-hub cannot be avoided in graphs with large treewidth: graphs containing no hole with a $2$-hub and no induced subgraph isomorphic to the basic obstructions have bounded treewidth. I will present a proof of this result\, and will also give an overview of related works.\nBased on joint work with Tara Abrishami\, Bogdan Alecu\, Maria Chudnovsky\, Sophie Spirkl and Kristina Vušković.
URL:https://dimag.ibs.re.kr/event/2022-07-07/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220704T163000
DTEND;TZID=Asia/Seoul:20220704T173000
DTSTAMP:20260417T081215
CREATED:20220704T073000Z
LAST-MODIFIED:20240707T075651Z
UID:5797-1656952200-1656955800@dimag.ibs.re.kr
SUMMARY:Eric Vigoda\, Computational phase transition and MCMC algorithms
DESCRIPTION:This talk will highlight recent results establishing a beautiful computational phase transition for approximate counting/sampling in (binary) undirected graphical models (such as the Ising model or on weighted independent sets). The computational problem is to sample from the equilibrium distribution of the model or equivalently approximate the corresponding normalizing factor known as the partition function. We show that when correlations die off on the infinite D-regular tree then the Gibbs sampler has optimal mixing time of $O(n \log n)$ on any graph of maximum degree D\, whereas when the correlations persist (in the limit) then the sampling/counting problem are NP-hard to approximate.  The Gibbs sampler is a simple Markov Chain Monte Carlo (MCMC) algorithm. Key to these mixing results are a new technique known as spectral independence which considers the pairwise influence of vertices. We show that spectral independence implies an optimal convergence rate for a variety of MCMC algorithms.
URL:https://dimag.ibs.re.kr/event/2022-07-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220629T163000
DTEND;TZID=Asia/Seoul:20220629T173000
DTSTAMP:20260417T081215
CREATED:20220611T121204Z
LAST-MODIFIED:20240705T171148Z
UID:5827-1656520200-1656523800@dimag.ibs.re.kr
SUMMARY:Xizhi Liu\, Hypergraph Turán problem: from 1 to ∞
DESCRIPTION:One interesting difference between (nondegenerate) Graph Turán problem and Hypergraph Turán problem is that the hypergraph families can have at least two very different extremal constructions. In this talk\, we will look at some recent progress and approaches to constructing hypergraph families with at least two different extremal constructions.\nBased on some joint work with Dhruv Mubayi\, Christian Reiher\, Jianfeng Hou\, Heng Li\, and Yixiao Zhang.
URL:https://dimag.ibs.re.kr/event/2022-06-29/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220627T163000
DTEND;TZID=Asia/Seoul:20220627T173000
DTSTAMP:20260417T081215
CREATED:20220627T073000Z
LAST-MODIFIED:20240707T075705Z
UID:5733-1656347400-1656351000@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Radial projections in finite space
DESCRIPTION:Given a set $E$ and a point $y$ in a vector space over a finite field\, the radial projection $\pi_y(E)$ of $E$ from $y$ is the set of lines that through $y$ and points of $E$. Clearly\, $|\pi_y(E)|$ is at most the minimum of the number of lines through $y$ and $|E|$. I will discuss several results on the general question: For how many points $y$ can $|\pi_y(E)|$ be much smaller than this maximum? \nThis is motivated by an analogous question in fractal geometry. The Hausdorff dimension of a radial projection of a set $E$ in $n$ dimensional real space will typically be the minimum of $n-1$ and the Hausdorff dimension of $E$. Several recent papers by authors including Matilla\, Orponen\, Liu\, Shmerikin\, and Wang consider the question: How large can the set of points with small radial projections be? This body of work has several important applications\, including recent progress on the Falconer distance conjecture. \nThis is joint with Thang Pham and Vu Thi Huong Thu.
URL:https://dimag.ibs.re.kr/event/2022-06-27/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220622T163000
DTEND;TZID=Asia/Seoul:20220622T173000
DTSTAMP:20260417T081215
CREATED:20220622T073000Z
LAST-MODIFIED:20240707T075717Z
UID:5846-1655915400-1655919000@dimag.ibs.re.kr
SUMMARY:Chengfei Xie\, On the packing densities of superballs in high dimensions
DESCRIPTION:The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk\, we give a new proof for the result that for $ 1<p<2 $\, the translative packing density of superballs (a generalization of $\ell^p$ balls) in $\mathbb{R}^n$ is $\Omega(n/2^n)$.\nThis is joint work with Gennian Ge.
URL:https://dimag.ibs.re.kr/event/2022-06-22/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220613T163000
DTEND;TZID=Asia/Seoul:20220613T173000
DTSTAMP:20260417T081215
CREATED:20220613T073000Z
LAST-MODIFIED:20240707T075724Z
UID:5578-1655137800-1655141400@dimag.ibs.re.kr
SUMMARY:Amadeus Reinald\, Twin-width and forbidden subdivisions
DESCRIPTION:Twin-width is a recently introduced graph parameter based on vertex contraction sequences. On classes of bounded twin-width\, problems expressible in FO logic can be solved in FPT time when provided with a sequence witnessing the bound. Classes of bounded twin-width are very diverse\, notably including bounded rank-width\, $\Omega ( \log (n) )$-subdivisions of graphs of size $n$\, and proper minor closed classes. In this talk\, we look at developing a structural understanding of twin-width in terms of induced subdivisions. \nStructural characterizations of graph parameters have mostly looked at graph minors\, for instance\, bounded tree-width graphs are exactly those forbidding a large wall minor. An analogue in terms of induced subgraphs could be that\, for sparse graphs\, large treewidth implies the existence of an induced subdivision of a large wall. However\, Sintiari and Trotignon have ruled out such a characterization by showing the existence of graphs with arbitrarily large girth avoiding any induced subdivision of a theta ($K_{2\,3}$). Abrishami\, Chudnovsky\, Hajebi and Spirkl have recently shown that such (theta\, triangle)-free classes have nevertheless logarithmic treewidth. \nAfter an introduction to twin-width and its ties to vertex orderings\, we show that theta-free graphs of girth at least 5 have bounded twin-width. \nJoint work with Édouard Bonnet\, Eun Jung Kim\, Stéphan Thomassé and Rémi Watrigant.
URL:https://dimag.ibs.re.kr/event/2022-06-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220602T161500
DTEND;TZID=Asia/Seoul:20220602T171500
DTSTAMP:20260417T081215
CREATED:20220602T071500Z
LAST-MODIFIED:20240705T172222Z
UID:5763-1654186500-1654190100@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\, Graph minor theory and beyond
DESCRIPTION:[Colloquium\, Department of Mathematical Sciences\, KAIST] \nOne of the important work in graph theory is the graph minor theory developed by Robertson and Seymour in 1980-2010. This provides a complete description of the class of graphs that do not contain a fixed graph H as a minor. Later on\, several generalizations of H-minor free graphs\, which are sparse\, have been defined and studied. Also\, similar topics on dense graph classes have been deeply studied. In this talk\, I will survey topics in graph minor theory\, and discuss related topics in structural graph theory.
URL:https://dimag.ibs.re.kr/event/2022-06-02-kwon/
LOCATION:Room 1501\, Bldg. E6-1\, KAIST
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220602T103000
DTEND;TZID=Asia/Seoul:20220602T113000
DTSTAMP:20260417T081215
CREATED:20220602T013000Z
LAST-MODIFIED:20240707T075917Z
UID:5595-1654165800-1654169400@dimag.ibs.re.kr
SUMMARY:Jeck Lim\, Sums of linear transformations
DESCRIPTION:We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions\, then\, for any finite subset $A$ of $\mathbb{Z}^d$\, \[ |L_1 A+L_2 A|\geq (|\det(L_1)|^{1/d}+|\det(L_2)|^{1/d})^d |A|- o(|A|).\] This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and $L_2$. As an application\, we prove a lower bound for $|A  + \lambda \cdot A|$ when $A$ is a finite set of real numbers and $\lambda$ is an algebraic number.\nJoint work with David Conlon.
URL:https://dimag.ibs.re.kr/event/2022-06-02/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220530T163000
DTEND;TZID=Asia/Seoul:20220530T173000
DTSTAMP:20260417T081215
CREATED:20220530T073000Z
LAST-MODIFIED:20240705T172232Z
UID:5495-1653928200-1653931800@dimag.ibs.re.kr
SUMMARY:Hongseok Yang (양홍석)\, Learning Symmetric Rules with SATNet
DESCRIPTION:SATNet is a differentiable constraint solver with a custom backpropagation algorithm\, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact\, SATNet has been successfully applied to learn\, among others\, the rules of a complex logical puzzle\, such as Sudoku\, just from input and output pairs where inputs are given as images. In this paper\, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet\, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries\, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik’s cube show the substantial improvement of SymSATNet over the baseline SATNet. \nThis is joint work with Sangho Lim and Eungyeol Oh.
URL:https://dimag.ibs.re.kr/event/2022-05-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220527T132000
DTEND;TZID=Asia/Seoul:20220527T174000
DTSTAMP:20260417T081215
CREATED:20220527T042000Z
LAST-MODIFIED:20240707T075940Z
UID:5555-1653657600-1653673200@dimag.ibs.re.kr
SUMMARY:KSIAM 2022 Spring Meeting
DESCRIPTION:KSIAM (Korean Society for Industrial and Applied Mathematics) will have the KSIAM 2022 Spring Conference at the Institute for Basic Science (IBS). Its academic session for Combinatorics decided to have an invited talk by Joonkyung Lee at the Hanyang University\, a special session “Graph Theory” organized by Sang-il Oum and the IBS DIMAG\, a special session “Enumerative Combinatorics” organized by Dongsu Kim at KAIST\, and a poster session\, all on May 27 afternoon. The deadline for the abstract submission is May 2 and the deadline for the early registration is May 9. \nInvited talk (May 27 Friday\, 16:40-17:40)\n\nJoonkyung Lee이준경 (Hanyang University)\, Graph homomorphism inequalities and their applications\nCounting (weighted) homomorphisms between graphs relates to a wide variety of areas\, in- cluding graph theory\, probability\, statistical physics and theoretical computer science. In recent years\, various new applications of inequalities between graph homomorphism counts have been found.\nWe will discuss some of the examples\, including a simple proof of the Bondy–Simonovits theorem and a new estimate for the rainbow Turán numbers of even cycles. If time permits\, we will also touch upon some recent progress on Sidorenko’s conjecture and related questions\, in particular their applications on the bipartite Turán problems.\nBased on joint work with David Conlon\, Jaehoon Kim\, Hong Liu\, and Tuan Tran. \n\nSpecial session “Graph Theory” (May 27\, 13:20-14:40)\nOrganized by Sang-il Oum엄상일 (IBS Discrete Mathematics Group & KAIST). \nSpeakers\n\nBoram Park박보람 (Ajou University)\, Odd Coloring of Graphs\nAn odd $c$-coloring of a graph is a proper $c$-coloring such that each non-isolated vertex has a color appearing an odd number of times on its neighborhood. Recently\, Cranston investigated odd colorings of graphs with bounded maximum average degree\, and conjectured that every graph $G$ with $\operatorname{mad}(G)\leq \frac{4c-4}{c+1}$ has an odd $c$-coloring for $c\geq 4$\, and proved the conjecture for $c\in\{5\, 6\}$. In particular\, planar graphs with girth at least $7$ and $6$ have an odd $5$-coloring and an odd $6$-coloring\, respectively.\nWe completely resolve Cranston’s conjecture. For $c\geq 7$\, we show that the conjecture is true\, in a stronger form that was implicitly suggested by Cranston\, but for $c=4$\, we construct counterexamples\, which all contain $5$-cycles. On the other hand\, we show that a graph $G$ with $\operatorname{mad}(G)<\frac{22}{9}$ and no induced $5$-cycles has an odd $4$-coloring. This implies that a planar graph with girth at least 11 has an odd $4$-coloring. We also prove that a planar graph with girth at least 5 has an odd $6$-coloring.\nJoint work with Eun-Kyung Cho\, Ilkyoo Choi\, and Hyemin Kown. \n\n\nJongyook Park박종육 (Kyungpook National University)\, On the Delsarte bound\nWe study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence\, we show that if a strongly regular graph contains a Delsarte clique\, then the parameter μ is either small or large. Furthermore\, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound\, we rule out an infinite family of feasible parameters (v\, k\, λ\, μ) for strongly regular graphs. Lastly\, we provide tables of parameters (v\, k\, λ\, μ) for nonexistent strongly regular graphs with smallest eigenvalue −4\,−5\,−6 or −7. This is joint work with Gary Greaves and Jack Koolen. \n\n\nO-joung Kwon권오정 (Hanyang University and IBS Discrete Mathematics Group)\, Well-partitioned chordal graphs\nWe introduce a new subclass of chordal graphs that generalizes the class of split graphs\, which we call well-partitioned chordal graphs. A connected graph $G$ is a well-partitioned chordal graph if there exist a partition $\mathcal{P}$ of the vertex set of $G$ into cliques and a tree $\mathcal{T}$ having $\mathcal{P}$ as a vertex set such that for distinct $X\,Y\in \mathcal{P}$\, (1) the edges between $X$ and $Y$ in $G$ form a complete bipartite subgraph whose parts are some subsets of $X$ and $Y$\, if $X$ and $Y$ are adjacent in $\mathcal{T}$\, and (2) there are no edges between $X$ and $Y$ in $G$ otherwise. A split graph with vertex partition $(C\, I)$ where $C$ is a clique and $I$ is an independent set is a well-partitioned chordal graph as witnessed by a star $\mathcal{T}$ having $C$ as the center and each vertex in $I$ as a leaf\, viewed as a clique of size $1$. We characterize well-partitioned chordal graphs by forbidden induced subgraphs\, and give a polynomial-time algorithm that given a graph\, either finds an obstruction\, or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal.\nWe observe that there are problems\, for instance Densest $k$-Subgraph and $b$-Coloring\, that are polynomial-time solvable on split graphs but become NP-hard on well-partitioned chordal graphs. On the other hand\, we show that the Geodetic Set problem\, known to be NP-hard on chordal graphs\, can be solved in polynomial time on well-partitioned chordal graphs. We also answer two combinatorial questions on well-partitioned chordal graphs that are open on chordal graphs\, namely that each well-partitioned chordal graph admits a polynomial-time constructible tree $3$-spanner\, and that each ($2$-connected) well-partitioned chordal graph has a vertex that intersects all its longest paths (cycles). Joint work with Jungho Ahn\, Lars Jaffke\, and Paloma T. Lima. \n\n\nStijn Cambie (IBS Extremal Combinatorics and Probability Group)\, Regular Cereceda’s Conjecture\nThe reconfiguration graph $\mathcal C_k(G)$ for the $k$-colourings of a graph $G$ has a vertex for each proper $k$-colouring of $G$\, and two vertices of $\mathcal C_k(G)$ are adjacent precisely when those $k$-colourings differ on a single vertex of $G$. Much work has focused on bounding the maximum value of $\operatorname{diam} \mathcal C_k(G)$ over all $n$-vertex graphs $G$. One of the most famous conjectures related related to $\mathcal C_k(G)$ is Cereceda’s conjecture\, which says that if $k \ge \operatorname{degen}(G) + 2$\, the diameter of $\mathcal C_k(G)$ is $O(n^2)$. In this talk\, we give some ideas towards a precise form for Cereceda’s conjecture\, when restricting to regular graphs. \nThis is based on joint work with Wouter Cames van Batenburg (TU Delft\, the Netherlands) and Daniel Cranston (Virginia Commonwealth University\, USA)\, which originates from the online workshop Graph Reconfiguration of the Sparse Graphs Coalition. \n\nSpecial session “Enumerative Combinatorics” (May 27\, 15:00-16:20)\nOrganized by Dongsu Kim김동수 (KAIST). \nSpeakers\n\nMeesue Yoo류미수 (Chungbuk National University)\, Combinatorial description for the Hall-Littlewood expansion of unicellular LLT and chromatic quasisymmetric polynomials\nIn this work\, we obtain a Hall–Littlewood expansion of the chromatic quasisymmetric functions by using a Dyck path model and linked rook placements. By using the Carlsson–Mellit relation between the chromatic quasisymmetric functions and the unicellular LLT polynomials\, this combinatorial description for the Hall–Littlewood coefficients of the chromatic quasisymmetric functions also gives the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall–Littlewood polynomials. Joint work with Seung Jin Lee. \n\n\nDonghyun Kim김동현 (Sungkyunkwan University)\, Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials\nThe Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$\, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the partially asymmetric simple exclusion process (PASEP) and they can be obtained as a specialization of the Askey-Wilson polynomials. We give two different combinatorial formulas for the coefficients of the (transformed) Al-Salam-Chihara polynomials. Our formulas make manifest the fact that the coefficients are polynomials in $\alpha$\, $\beta$ and $q$ with positive coefficients. \n\n\nJisun Huh허지선 (Ajou University)\, Combinatorics on bounded Motzkin paths and its applications\nA free Motzkin path of length \(n\) is a lattice path which starts at \((0\,0)\) or \((0\,1)\)\, ends at \((n\,0)\)\, and has only up steps \(u=(1\,1)\)\, down steps \(d=(1\,-1)\)\, and flat steps \(f=(1\,0)\). In addition\, if a free Motzkin path starts at \((0\,0)\) and stays weakly above the \(x\)-axis\, then it is called a Motzkin path. In this talk\, we construct a bijection between \(F(m\,r\,k)\) and \(M(m\,r\,k)\)\, where \(F(m\,r\,k)\) is the set of free Motzkin paths of length \(m+r\) with \(r\) flat steps that are contained in the strip \(-\lfloor k/2 \rfloor \leq y \leq \lfloor (k+1)/2 \rfloor\) and \(M(m\,r\,k)\) is the set of Motzkin prefixed of length \(m+r\) with \(r\) flat steps that are contained in the strip \(0 \leq y \leq k\). Furthermore\, we provide path interpretations of ordinary/self-conjugate \(t\)-core partitions with \(m\)-corners as an application.\nThis is joint work with Hyunsoo Cho\, Hayan Nam\, and Jaebum Sohn. \n\n\nJihyeug Jang장지혁 (Sungkyunkwan University)\, A combinatorial model for the transition matrix between the Specht and web bases\nWe introduce a new class of permutations\, called web permutations. Using these permutations\, we provide a combinatorial interpretation for entries of the transition between the Specht and web bases\, which answers Rhoades’s question. Furthermore\, we study enumerative properties of these permutations. Joint work with Byung-Hak Hwang and Jaeseong Oh.
URL:https://dimag.ibs.re.kr/event/ksiam-2022-spring-meeting/
LOCATION:IBS Science Culture Center
CATEGORIES:Workshops and Conferences
ATTACH;FMTTYPE=image/png:https://dimag.ibs.re.kr/cms/wp-content/uploads/2022/05/main_ss20220329.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220525T163000
DTEND;TZID=Asia/Seoul:20220525T173000
DTSTAMP:20260417T081215
CREATED:20220525T073000Z
LAST-MODIFIED:20240705T172235Z
UID:5509-1653496200-1653499800@dimag.ibs.re.kr
SUMMARY:Sebastian Siebertz\, Transducing paths in graph classes with unbounded shrubdepth
DESCRIPTION:Transductions are a general formalism for expressing transformations of graphs (and more generally\, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is\, has bounded shrubdepth) if\, and only if\, from C one cannot FO-transduce the class of all paths. This establishes one of the three remaining open questions posed by Blumensath and Courcelle about the MSO-transduction quasi-order\, even in the stronger form that concerns FO-transductions instead of MSO-transductions. \nThe backbone of our proof is a graph-theoretic statement that says the following: If a graph G excludes a path\, the bipartite complement of a path\, and a half-graph as semi-induced subgraphs\, then the vertex set of G can be partitioned into a bounded number of parts so that every part induces a cograph of bounded height\, and every pair of parts semi-induce a bi-cograph of bounded height. This statement may be of independent interest; for instance\, it implies that the graphs in question form a class that is linearly chi-bounded. \nThis is joint work with Patrice Ossona de Mendez and Michał Pilipczuk.
URL:https://dimag.ibs.re.kr/event/2022-05-25/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220523T163000
DTEND;TZID=Asia/Seoul:20220523T173000
DTSTAMP:20260417T081215
CREATED:20220523T073000Z
LAST-MODIFIED:20240705T172235Z
UID:5451-1653323400-1653327000@dimag.ibs.re.kr
SUMMARY:Stijn Cambie\, The precise diameter of reconfiguration graphs
DESCRIPTION:Reconfiguration is about changing instances in small steps. For example\, one can perform certain moves on a Rubik’s cube\, each of them changing its configuration a bit. In this case\, in at most 20 steps\, one can end up with the preferred result. One could construct a graph with as nodes the possible configurations of the Rubik’s cube (up to some isomorphism) and connect two nodes if one can be obtained by applying only one move to the other. Finding an optimal solution\, i.e. a minimum number of moves to solve a Rubik’s cube is now equivalent to finding the distance in the graph. \nWe will wonder about similar problems in reconfiguration\, but applied to list- and DP-colouring. In this case\, the small step consists of recolouring precisely one vertex. Now we will be interested in the diameter of the reconfiguration graph and show that sometimes we can determine the precise diameters of these. \nAs such\, during this talk\, we present some main ideas of [arXiv:2204.07928].
URL:https://dimag.ibs.re.kr/event/2022-05-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220519T161500
DTEND;TZID=Asia/Seoul:20220519T171500
DTSTAMP:20260417T081215
CREATED:20220519T071500Z
LAST-MODIFIED:20240707T080000Z
UID:5661-1652976900-1652980500@dimag.ibs.re.kr
SUMMARY:Gil Kalai\, The Cascade Conjecture and other Helly-type Problems
DESCRIPTION:[Colloquium\, Department of Mathematical Sciences\, KAIST] \nFor a set $X$ of points $x(1)$\, $x(2)$\, $\ldots$\, $x(n)$ in some real vector space $V$ we denote by $T(X\,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$.\nWe let $t(X\,r)=1+\dim(T(X\,r))$. \nRadon’s theorem asserts that\nIf $t(X\,1)< |X|$\, then $t(X\, 2) >0$. \nThe first open case of the cascade conjecture asserts that\nIf $t(X\,1)+t(X\,2) < |X|$\, then $t(X\,3) >0$. \nIn the lecture\, I will discuss connections with topology and with various problems in graph theory. I will also mention questions regarding dimensions of intersection of convex sets. \nSome related material:\n1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos\n2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804\n3) A link to Barany’s book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097
URL:https://dimag.ibs.re.kr/event/2022-05-19/
LOCATION:Zoom ID: 868 7549 9085
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220518T163000
DTEND;TZID=Asia/Seoul:20220518T173000
DTSTAMP:20260417T081215
CREATED:20220518T073000Z
LAST-MODIFIED:20240705T173008Z
UID:5506-1652891400-1652895000@dimag.ibs.re.kr
SUMMARY:Jan Kurkofka\, Canonical Graph Decompositions via Coverings
DESCRIPTION:We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph\, as determined by the relative position of these parts\, is described by a coarser model. This is a simpler graph determined entirely by the decomposition\, not imposed. \nThe model and decomposition are obtained as projections of the tangle-tree structure of a covering of the given graph that reflects its local structure at the intended level of locality while unfolding its global structure. \nOur theorem extends to locally finite quasi-transitive graphs and in particular to locally finite Cayley graphs. It thereby offers a canonical decomposition theorem for finitely generated groups into local parts\, whose relative structure is displayed by a graph. \nJoint work with Reinhard Diestel\, Raphael W. Jacobs and Paul Knappe.
URL:https://dimag.ibs.re.kr/event/2022-05-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220516T163000
DTEND;TZID=Asia/Seoul:20220516T173000
DTSTAMP:20260417T081216
CREATED:20220516T073000Z
LAST-MODIFIED:20240707T080014Z
UID:5553-1652718600-1652722200@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, A colorful version of the Goodman-Pollack-Wenger transversal theorem
DESCRIPTION:Hadwiger’s transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in $\mathbb{R}^d$ by Goodman\, Pollack\, and Wenger. Here we establish a colorful extension of their theorem\, which proves a conjecture of Arocha\, Bracho\, and Montejano. The proof uses topological methods\, in particular the Borsuk-Ulam theorem. The same methods also allow us to generalize some colorful transversal theorems of Montejano and Karasev.
URL:https://dimag.ibs.re.kr/event/2022-05-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR