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:20210101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220602T103000
DTEND;TZID=Asia/Seoul:20220602T113000
DTSTAMP:20260419T093750
CREATED:20220602T013000Z
LAST-MODIFIED:20240707T075917Z
UID:5595-1654165800-1654169400@dimag.ibs.re.kr
SUMMARY:Jeck Lim\, Sums of linear transformations
DESCRIPTION:We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions\, then\, for any finite subset $A$ of $\mathbb{Z}^d$\, \[ |L_1 A+L_2 A|\geq (|\det(L_1)|^{1/d}+|\det(L_2)|^{1/d})^d |A|- o(|A|).\] This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and $L_2$. As an application\, we prove a lower bound for $|A  + \lambda \cdot A|$ when $A$ is a finite set of real numbers and $\lambda$ is an algebraic number.\nJoint work with David Conlon.
URL:https://dimag.ibs.re.kr/event/2022-06-02/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
END:VCALENDAR