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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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
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DTSTART:20240101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250617T163000
DTEND;TZID=Asia/Seoul:20250617T173000
DTSTAMP:20260416T221850
CREATED:20250428T140029Z
LAST-MODIFIED:20250428T140029Z
UID:10877-1750177800-1750181400@dimag.ibs.re.kr
SUMMARY:Attila Jung\, The Quantitative Fractional Helly Theorem
DESCRIPTION:Two celebrated extensions of Helly’s theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Barany\, Katchalski\, and Pach (1982). Improving on several recent works\, we prove an optimal combination of these two results. We show that given a family $F$ of $n$ convex sets in $\mathbb{R}^d$ such that at least $\alpha \binom{n}{d+1}$ of the $(d+1)$-tuples of $F$ have an intersection of volume at least 1\, then one can select $\Omega_{d\,\alpha}(n)$ members of $F$ whose intersection has volume at least $\Omega_d(1)$. Joint work with Nora Frankl and Istvan Tomon.
URL:https://dimag.ibs.re.kr/event/2025-06-17/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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