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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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DTSTART;TZID=Asia/Seoul:20260901T163000
DTEND;TZID=Asia/Seoul:20260901T173000
DTSTAMP:20260825T042634Z
CREATED:20260801T015407Z
LAST-MODIFIED:20260825T042634Z
UID:13026-1788280200-1788283800@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Incidences between points and n-flats in PG(n+d\,q)
DESCRIPTION:Let $P$ be a set of points in $PG(n+d\,q)$\, and let $L$ be a set of $n$-flats. Here\, $n$-flat is a short name for $n$-dimensional projective subspaces. A classical bound of Haemers\, rediscovered in an influential paper of Vinh\, gives an upper bound on the difference between the number of incidences between $P$ and $L$ and the expected number of incidences for random sets of points and flats with the same cardinalities as $P$ and $L$. Haemers’ bound is tight as a function of $|P|$ times $|L|$. Recent work of Kong and Tamo improves the bound under the assumption that $|L|$ is not too large. I will discuss recent work\, joint with Tao Zhang\, that improves the bound of Kong and Tamo. The proof depends on an independently interesting upper bound on the number of pairs $(l_1\,l_2)$ of flats in $L$ such that $\dim(l_1 \cap l_2)=j$\, for $0 \leq j \leq n$.
URL:https://dimag.ibs.re.kr/event/2026-09-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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