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CATEGORIES:Combinatorics and Probability seminar
SUMMARY:Covering real grids with multiplicity - Simona Boy
adzhiyska\, Birmingham
DTSTART:20230518T140000Z
DTEND:20230518T150000Z
UID:TALK5191AT
URL:/talk/index/5191
DESCRIPTION:Given a field $\\mathbb{F}$\, finite subsets $S_1\
,\\dots\,S_d\\subseteq \\mathbb{F}$\, and a point
$\\vec{p}\\in S_1\\times \\dots\\times S_d$\,\nwha
t is the smallest number of hyperplanes needed to
cover all points of $S_1\\times\\dots\\times S_d\\
setminus\\{\\vec{p}\\}\\subseteq \\mathbb{F}^d$ wh
ile omitting $\\vec{p}$? This question was answere
d precisely in a celebrated paper of Alon and F\\"
uredi.\n\nWe will discuss a variant of this proble
m in which every point in $S_1\\times\\dots\\time
s S_d\\setminus\\{\\vec{p}\\}$ must be covered \\e
mph{at least $k\\geq 1$ times}\, while the remaini
ng point $\\vec{p}$ is again left uncovered.\nIn c
ontrast to the case $k=1$\, this problem is genera
lly not well understood for larger $k$.\nRecently
Clifton and Huang and Sauermann and Wigderson inve
stigated the special case where $\\mathbb{F} = \\m
athbb{R}$ and the grid is $\\{0\,1\\}^d$. A natura
l next step is to consider larger grids over the r
eals. In this talk\, we will focus on the two-dime
nsional setting and determine the answer for sever
al different types of grids.\n\nThis is joint work
with Anurag Bishnoi\, Shagnik Das\, and Yvonne de
n Bakker.\n
LOCATION:Arts LR1
CONTACT:Dr Richard Mycroft
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