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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
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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20201021T163000
DTEND;TZID=Asia/Seoul:20201021T173000
DTSTAMP:20260419T190907
CREATED:20200930T112510Z
LAST-MODIFIED:20240707T082519Z
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SUMMARY:Joonkyung Lee (이준경)\, On graph norms for complex-valued functions
DESCRIPTION:For any given graph $H$\, one may define a natural corresponding functional $\|.\|_H$ for real-valued functions by using homomorphism density. One may also extend this to complex-valued functions\, once $H$ is paired with a $2$-edge-colouring $\alpha$ to assign conjugates. We say that $H$ is real-norming (resp. complex-norming) if $\|.\|_H$ (resp. there is $\alpha$ such that $\|.\|_{H\,\alpha}$) is a norm on the vector space of real-valued (resp. complex-valued) functions. This generalises Gowers norms\, a widely used tool in extremal combinatorics to quantify quasirandomness. \nWe unify these two seemingly different notions of graph norms in real- and complex-valued settings\, by proving that $H$ is complex-norming if and only if it is real-norming. Our proof does not explicitly construct a suitable $2$-edge-colouring $\alpha$ but obtain its existence and uniqueness\, which may be of independent interest. \nAs an application\, we give various example graphs that are not norming. In particular\, we show that hypercubes are not norming\, which answers the only question appeared in Hatami’s pioneering work in the area that remained untouched. This is joint work with Alexander Sidorenko.
URL:https://dimag.ibs.re.kr/event/2020-10-21/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201027T163000
DTEND;TZID=Asia/Seoul:20201027T173000
DTSTAMP:20260419T190907
CREATED:20201009T013533Z
LAST-MODIFIED:20240707T082504Z
UID:3107-1603816200-1603819800@dimag.ibs.re.kr
SUMMARY:Jeong Ok Choi (최정옥)\, Various game-theoretic models on graphs
DESCRIPTION:We introduce some of well-known game-theoretic graph models and related problems. \nA contagion game model explains how an innovation diffuses over a given network structure and focuses on finding conditions on which structure an innovation becomes epidemic. Regular infinite graphs are interesting examples to explore. We show that regular infinite trees make an innovation least advantageous to be epidemic considering the whole class of infinite regular graphs. \nA network creation game model\, on the other hand\, tries to explain the dynamics on forming a network structure when each vertex plays independently and selfishly. An important question is how costly a formation can be made without any central coordination\, and the concept of Price of Anarchy (PoA) is introduced. In the model originally suggested by Fabrikant et al.\, PoA measures how bad the forming cost can be at Nash equilibria compared to absolute minimum\, and they conjectured that this inefficiency can happen only when some tree structures are formed (Tree Conjecture). We will introduce recent progress on this tree conjecture\, remaining open problems\, and possible variations. \nThis talk includes part of joint work with Unjong Yu.
URL:https://dimag.ibs.re.kr/event/2020-10-27/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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