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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20230101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241008T163000
DTEND;TZID=Asia/Seoul:20241008T173000
DTSTAMP:20260415T183345
CREATED:20240815T140405Z
LAST-MODIFIED:20240815T140630Z
UID:9708-1728405000-1728408600@dimag.ibs.re.kr
SUMMARY:Mathias Schacht\, Canonical colourings in random graphs
DESCRIPTION:Rödl and Ruciński established Ramsey’s theorem for random graphs. In particular\, for fixed integers $r$\, $\ell\geq 2$ they showed that $n^{-\frac{2}{\ell+1}}$ is a threshold for the Ramsey property that every $r$-colouring of the edges of the binomial random graph $G(n\,p)$ yields a monochromatic copy of $K_\ell$. \nWe investigate how this result extends to arbitrary colourings of $G(n\,p)$ with an unbounded number of colours. In this situation Erdős and Rado showed that canonically coloured copies of $K_\ell$ can be ensured in the deterministic setting.\nWe transfer the Erdős-Rado theorem to the random environment and show that for $\ell\geq 4$ both thresholds coincide. As a consequence the proof yields $K_{\ell+1}$-free graphs $G$ for which every edge colouring yields a canonically coloured $K_\ell$. \nThis is joint work with Nina Kamčev.
URL:https://dimag.ibs.re.kr/event/2024-10-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241015T163000
DTEND;TZID=Asia/Seoul:20241015T173000
DTSTAMP:20260415T183345
CREATED:20240728T055631Z
LAST-MODIFIED:20240815T135958Z
UID:9631-1729009800-1729013400@dimag.ibs.re.kr
SUMMARY:Kyeongsik Nam (남경식)\, Random walks on percolation
DESCRIPTION:In general\, random walks on fractal graphs are expected to exhibit anomalous behaviors\, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach in 1982 conjectured that random walks on critical percolation\, a prominent example of fractal graphs\, exhibit mean field behavior; for instance\, its spectral dimension is 4/3. In this talk\, I will talk about this conjecture for a canonical dependent percolation model.
URL:https://dimag.ibs.re.kr/event/2024-10-15/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241022T163000
DTEND;TZID=Asia/Seoul:20241022T173000
DTSTAMP:20260415T183345
CREATED:20240905T081105Z
LAST-MODIFIED:20240913T030403Z
UID:9850-1729614600-1729618200@dimag.ibs.re.kr
SUMMARY:Colin Geniet\, Permutations\, patterns\, and twin-width
DESCRIPTION:This talk will first introduce combinatorics on permutations and patterns\, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given pattern\, and the Guillemot-Marx algorithm for pattern detection using the notion now known as twin-width. \nI will then present a decomposition result: permutations avoiding a pattern factor into bounded products of separable permutations. This can be rephrased in terms of twin-width: permutation with bounded twin-width are build from a bounded product of permutations of twin-width 0. Comparable results on graph encodings follow from this factorisation. \nThis is joint work with Édouard Bonnet\, Romain Bourneuf\, and Stéphan Thomassé.
URL:https://dimag.ibs.re.kr/event/2024-10-22/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241029T163000
DTEND;TZID=Asia/Seoul:20241029T173000
DTSTAMP:20260415T183345
CREATED:20240919T043705Z
LAST-MODIFIED:20240919T043705Z
UID:9894-1730219400-1730223000@dimag.ibs.re.kr
SUMMARY:Felix Christian Clemen\, Triangles in the Plane
DESCRIPTION:A classical problem in combinatorial geometry\, posed by Erdős in 1946\, asks to determine the maximum number of unit segments in a set of $n$ points in the plane. Since then a great variety of extremal problems in finite planar point sets have been studied. Here\, we look at such questions concerning triangles. Among others we answer the following question asked by Erdős and Purdy almost 50 years ago: Given $n$ points in the plane\, how many triangles can be approximate congruent to equilateral triangles? \nFor our proofs we use hypergraph Turán theory. This is joint work with Balogh and Dumitrescu.
URL:https://dimag.ibs.re.kr/event/2024-10-29/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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