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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20220101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230809T100000
DTEND;TZID=Asia/Seoul:20230809T160000
DTSTAMP:20260419T022248
CREATED:20230802T144334Z
LAST-MODIFIED:20240707T073343Z
UID:7441-1691575200-1691596800@dimag.ibs.re.kr
SUMMARY:2023 Mini-Workshop on Discrete Geometry
DESCRIPTION:2023 Mini-Workshop on Discrete Geometry will be held on August 9th at Room B332\, Institute for Basic Science (IBS)\, Daejeon\, Republic of Korea. \nThe workshop consists of three presentations on recent results and an open problem session. \nResearchers who are highly interested in this field are welcome to attend. \nTentative schedule\n\n10:00-10:50 Michael Dobbins (SUNY Binghamton): Colorful intersections\, Tverberg partitions\, and geometric transversals\n11:00-11:30 Andreas Holmsen (KAIST): The topology of the complex of ordered partitions\n11:30-13:30 Lunch and free discussion\n13:30-14:10 Minki Kim김민기 (GIST): Some variants of the colorful Helly theorems\n14:20-16:00 Open problem session\n16:30-17:30 Discrete Math Seminar: R. Amzi Jeffs (Carnegie Mellon University)\n\nOrganizers\n\nAndreas Holmsen (KAIST)\nJinha Kim김진하 (IBS Discrete Mathematics Group)\nMinki Kim김민기 (GIST)\nSang-il Oum엄상일 (IBS Discrete Mathematics Group / KAIST)\n\nAbstracts\nMichael Dobbins (SUNY Binghamton): Colorful intersections\, Tverberg partitions\, and geometric transversals\nGiven three red convex sets and three blue convex sets in three-dimensional space\, suppose every red set intersects every blue set. Montejano’s theorem says there is a line that intersects all the red sets or all the blue sets. This was generalized to k-transversals in $\mathbb R^d$ by Montejano and Karasev using sophisticated algebraic and topological tools. Here we give further generalizations based on more accessible methods such as the test-map/configuration space scheme\, Sarkaria’s tensor method\, and discrete Morse theory. \nAndreas Holmsen (KAIST): The topology of the complex of ordered partitions\nThe set of partitions of {1\,…\,n} into k nonempty ordered parts can be equipped with a natural cell-complex structure which we denote by P(n\,k). Here we use discrete Morse theory to show that P(n\,k) is homotopy equivalent to a wedge of (n-k)-dimensional spheres\, where the number of spheres is given in terms of Stirling numbers of the second kind. Our result has applications related to geometric transversals and Tverberg partitions. \nMinki Kim (GIST): Some variants of the colorful Helly theorems\n\nGiven a finite family $F$ of nonempty sets\, the nerve of $F$ is the simplicial complex on $F$ whose simplices are precisely the intersecting subfamilies of $F$. The colorful Helly theorem\, which generalizes Helly’s theorem\, asserts the following: if $X$ is the nerve of the disjoint union of $d+1$ many finite families $F_1\,\ldots\,F_{d+1}$ of convex sets in $\mathbb{R}^d$ where each $F_i$ is not a simplex in $X$\, then there is a colorful $(d+1)$-tuple that is not a simplex of $X$. It was shown by Kalai and Meshulam that the same statement holds for $d$-collapsible/Leray complexes. In this talk\, I will explain the notion of $d$-collapsibility and $d$-Lerayness of simplicial complexes\, and present recent results on variants of the colorful Helly theorem and applications. This is based on joint work with Alan Lew.
URL:https://dimag.ibs.re.kr/event/2023-discrete-geometry/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230809T163000
DTEND;TZID=Asia/Seoul:20230809T173000
DTSTAMP:20260419T022248
CREATED:20230403T234729Z
LAST-MODIFIED:20240705T164149Z
UID:6963-1691598600-1691602200@dimag.ibs.re.kr
SUMMARY:R. Amzi Jeffs\, Intersection patterns of convex sets
DESCRIPTION:How can one arrange a collection of convex sets in d-dimensional Euclidean space? This guiding question is fundamental in discrete geometry\, and can be made concrete in a variety of ways\, for example the study of hyperplane arrangements\, embeddability of simplicial complexes\, Helly-type theorems\, and more. This talk will focus on the classical topic of d-representable complexes and its more recent generalization to convex codes. We will show how these frameworks differ\, share some novel Helly-type results\, and offer several tantalizing open questions.
URL:https://dimag.ibs.re.kr/event/2023-08-09/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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