BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20240101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20251118T163000
DTEND;TZID=Asia/Seoul:20251118T173000
DTSTAMP:20260416T124010
CREATED:20251016T022138Z
LAST-MODIFIED:20251104T135407Z
UID:11731-1763483400-1763487000@dimag.ibs.re.kr
SUMMARY:Fedor Noskov\, Polynomial dependencies in hypergraph Turan-type problems
DESCRIPTION:Consider a general Turan-type problem on hypergraphs. Let $\mathcal{F}$ be a family of $k$-subsets of $[n]$ that does not contain sets $F_1\, \ldots\, F_s$ satisfying some property $P$. We show that if $P$ is low-dimensional in some sense (e.g.\, is defined by intersections of bounded size) then\, under polynomial dependencies between $n\, k$ and the parameters of $P$\, one can reduce the problem of maximizing the size of the family $|\mathcal{F}|$ to a finite extremal set theory problem independent of $n$ and $k$. We show that our technique implies new bounds in a number of Turan-type problems including the Erdős-Sós forbidden intersection problem\, the Duke-Erdős forbidden sunflower problem\, forbidden $(t\, d)$-simplex problem and the forbidden hypergraph problem. Furthermore\, we also briefly discuss the connection between the aforementioned reduction and the measure boosting argument based on the action of a certain semigroup on the Boolean cube.  This connection turns out to be fruitful when extending extremal set theory problems to domains different from $\binom{[n]}{k}$. \nJoint work with Liza Iarovikova\, Andrey Kupavskii\, Georgy Sokolov and Nikolai Terekhov
URL:https://dimag.ibs.re.kr/event/2025-11-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR