BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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:20180101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191022T163000
DTEND;TZID=Asia/Seoul:20191022T173000
DTSTAMP:20260422T195816
CREATED:20190920T222518Z
LAST-MODIFIED:20240707T090027Z
UID:1407-1571761800-1571765400@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, On some properties of graph norms
DESCRIPTION:For a graph $H$\, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$\, $p\geq e(H)$\, denoted by $t_H(W)$. One may then define corresponding functionals $\|W\|_{H}:=|t_H(W)|^{1/e(H)}$ and $\|W\|_{r(H)}:=t_H(|W|)^{1/e(H)}$ and say that $H$ is (semi-)norming if $\|.\|_{H}$ is a (semi-)norm and that $H$ is weakly norming if $\|.\|_{r(H)}$ is a norm. \nWe obtain some results that contribute to the theory of (weakly) norming graphs. Firstly\, we show that ‘twisted’ blow-ups of cycles\, which include $K_{5\,5}\setminus C_{10}$ and $C_6\square K_2$\, are not weakly norming. This answers two questions of Hatami\, who asked whether the two graphs are weakly norming. Secondly\, we prove that $\|.\|_{r(H)}$ is not uniformly convex nor uniformly smooth\, provided that $H$ is weakly norming. This answers another question of Hatami\, who estimated the modulus of convexity and smoothness of $\|.\|_{H}$. We also prove that every graph $H$ without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of $H$ when studying graph norms. Based on joint work with Frederik Garbe\, Jan Hladký\, and Bjarne Schülke.
URL:https://dimag.ibs.re.kr/event/2019-10-22/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR