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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
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:20190101T000000
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DTSTART;TZID=Asia/Seoul:20200115T163000
DTEND;TZID=Asia/Seoul:20200115T173000
DTSTAMP:20260420T145924
CREATED:20200107T040041Z
LAST-MODIFIED:20240707T084237Z
UID:1990-1579105800-1579109400@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Furstenberg sets over finite fields
DESCRIPTION:An important family of incidence problems are discrete analogs of deep questions in geometric measure theory. Perhaps the most famous example of this is the finite field Kakeya conjecture\, proved by Dvir in 2008. Dvir’s proof introduced the polynomial method to incidence geometry\, which led to the solution to many long-standing problems in the area.\nI will talk about a generalization of the Kakeya conjecture posed by Ellenberg\, Oberlin\, and Tao. A $(k\,m)$-Furstenberg set S in $\mathbb F_q^n$ has the property that\, parallel to every affine $k$-plane V\, there is a k-plane W such that $|W \cap S| > m$. Using sophisticated ideas from algebraic geometry\, Ellenberg and Erman showed that if S is a $(k\,m)$-Furstenberg set\, then $|S| > c m^{n/k}$\, for a constant c depending on n and k. In recent joint work with Manik Dhar and Zeev Dvir\, we give simpler proofs of stronger bounds. For example\, if $m>2^{n+7}q$\, then $|S|=(1-o(1))mq^{n-k}$\, which is tight up to the $o(1)$ term.
URL:https://dimag.ibs.re.kr/event/2020-01-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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