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:20210101T000000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20220602T103000 DTEND;TZID=Asia/Seoul:20220602T113000 DTSTAMP:20260419T075233 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 BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20220622T163000 DTEND;TZID=Asia/Seoul:20220622T173000 DTSTAMP:20260419T075233 CREATED:20220622T073000Z LAST-MODIFIED:20240707T075717Z UID:5846-1655915400-1655919000@dimag.ibs.re.kr SUMMARY:Chengfei Xie\, On the packing densities of superballs in high dimensions DESCRIPTION:The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk\, we give a new proof for the result that for $ 1