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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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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260818T163000
DTEND;TZID=Asia/Seoul:20260818T173000
DTSTAMP:20260730T134943Z
CREATED:20260326T020259Z
LAST-MODIFIED:20260730T134943Z
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SUMMARY:Jinyoung Park (박진영)\, A reformulation of Talagrand's Discrete Convexity Conjecture
DESCRIPTION:The “Convexity Conjecture” by Talagrand asks\, roughly speaking\, whether one can “create convexity” in a bounded number of steps regardless of the dimension of the ambient space. Talagrand also proposed a discrete version of this conjecture\, calling it his “lifetime favorite problem” and offering a $1\,000 prize for its solution. While the continuous version of the conjecture was recently proven by Hua\, Song\, and Tudose\, the discrete analogue remains wide open. In this talk\, we introduce a reformulation of the discrete convexity conjecture using the new notion of “k-thresholds\,” an extension of the traditional definition of thresholds. Using this framework\, we establish the conjecture for several special cases\, focusing primarily on graph properties.
URL:https://dimag.ibs.re.kr/event/2026-08-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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DTSTART;TZID=Asia/Seoul:20260901T163000
DTEND;TZID=Asia/Seoul:20260901T173000
DTSTAMP:20260801T015407Z
CREATED:20260801T015407Z
LAST-MODIFIED:20260801T015407Z
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SUMMARY:Ben Lund\, TBA
DESCRIPTION:
URL:https://dimag.ibs.re.kr/event/2026-09-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260922T163000
DTEND;TZID=Asia/Seoul:20260922T173000
DTSTAMP:20260802T034024Z
CREATED:20260717T080520Z
LAST-MODIFIED:20260802T034024Z
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SUMMARY:David Wood\, Proof of the Clustered Hadwiger Conjecture
DESCRIPTION:Hadwiger famously conjectured that every $K_h$-minor-free graph is properly $(h-1)$-colourable. This talk will present the following improper analogue of Hadwiger’s Conjecture: for fixed $h$\, every $K_h$-minor-free graph is $(h-1)$-colourable with monochromatic components of bounded size. The number of colours is best possible regardless of the size of monochromatic components. This solves an open problem of Edwards\, Kang\, Kim\, Oum and Seymour [SIAM J. Disc. Math. 2015]\, and concludes a line of research initiated in 2007. Similarly\, for fixed $t\geqslant s$\, we show that every $K_{s\,t}$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is best possible\, solving an open problem of van de Heuvel and Wood [J. London Math. Soc. 2018]. We actually prove a single theorem from which both of the above results are immediate corollaries. For an excluded apex minor\, the result is strengthened  as follows: for fixed $t \geqslant s \geqslant 3$\, and for any fixed apex graph $X$\, every $K_{s\,t}$-subgraph-free $X$-minor-free graph is $(s+1)$-colourable with monochromatic components of bounded size. The number of colours is again best possible. This is joint work with Vida Dujmović\, Louis Esperet and Pat Morin [arXiv:2306.06224].
URL:https://dimag.ibs.re.kr/event/2026-09-22/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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