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UID:4c2ab2119c9ecbbbf2140afa33d3701f
CATEGORIES:Discrete Math
CREATED:20251020T215842
SUMMARY:Lior Gishboliner - VC-dimension for hypergraphs: improved bounds 
LOCATION:Hill 705
DESCRIPTION:Speaker: Lior Gishboliner (https://sites.google.com/view/lior-gishboliner) 
 (University of Toronto)\nTitle: VC-dimension for hypergraphs: improved boun
 ds \nAbstract: VC-dimension is an important notion with several application
 s in graph theory. A fundamental result is that graphs of bounded VC dimens
 ion have (small) homogeneous vertex-partitions, i.e., partitions where almo
 st every pair of parts has density close to 0 or 1. Recently, Chernikov and
  Towsner proved a hypergraph generalization of this fact. The quantitative 
 aspects of their result remain open. I will present some recent progress on
  this problem, answering two questions of Terry. This is a joint work with 
 Asaf Shapira and Yuval Wigderson. \n
X-ALT-DESC;FMTTYPE=text/html:<p dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-bottom: 0pt;
 "><span style="font-size: 11pt; font-family: Lato; color: #000000; backgrou
 nd-color: transparent; font-weight: bold; font-style: normal; font-variant:
  normal; text-decoration: none; vertical-align: baseline; white-space: pre-
 wrap;">Speaker:</span><span style="font-size: 10pt; font-family: Lato; colo
 r: #000000; background-color: transparent; font-weight: bold; font-style: n
 ormal; font-variant: normal; text-decoration: none; vertical-align: baselin
 e; white-space: pre-wrap;"> </span><span style="font-size: 11pt; font-famil
 y: Lato; color: #000000; background-color: transparent; font-weight: 400; f
 ont-style: normal; font-variant: normal; text-decoration: none; vertical-al
 ign: baseline; white-space: pre-wrap;"></span><a href="https://sites.google
 .com/view/lior-gishboliner" style="text-decoration: none;"><span style="fon
 t-size: 11pt; font-family: Lato; color: #cc0000; background-color: transpar
 ent; font-weight: 400; font-style: normal; font-variant: normal; text-decor
 ation: underline; vertical-align: baseline; white-space: pre-wrap;">Lior Gi
 shboliner</span></a><span style="font-size: 11pt; font-family: Lato; color:
  #000000; background-color: transparent; font-weight: 400; font-style: norm
 al; font-variant: normal; text-decoration: none; vertical-align: baseline; 
 white-space: pre-wrap;"> (University of Toronto)</span></p><p dir="ltr" sty
 le="line-height: 1.38; margin-top: 9pt; margin-bottom: 10pt;"><span style="
 font-size: 11pt; font-family: Lato; color: #000000; background-color: trans
 parent; font-weight: bold; font-style: normal; font-variant: normal; text-d
 ecoration: none; vertical-align: baseline; white-space: pre-wrap;">Title</s
 pan><span style="font-size: 11pt; font-family: Lato; color: #000000; backgr
 ound-color: transparent; font-weight: 400; font-style: normal; font-variant
 : normal; text-decoration: none; vertical-align: baseline; white-space: pre
 -wrap;">: VC-dimension for hypergraphs: improved bounds&nbsp;</span></p><p 
 dir="ltr" style="line-height: 1.38; margin-top: 9pt; margin-bottom: 0pt;"><
 span style="font-size: 11pt; font-family: Lato; color: #000000; background-
 color: transparent; font-weight: bold; font-style: normal; font-variant: no
 rmal; text-decoration: none; vertical-align: baseline; white-space: pre-wra
 p;">Abstract</span><span style="font-size: 11pt; font-family: Lato; color: 
 #000000; background-color: transparent; font-weight: 400; font-style: norma
 l; font-variant: normal; text-decoration: none; vertical-align: baseline; w
 hite-space: pre-wrap;">: VC-dimension is an important notion with several a
 pplications in graph theory. A fundamental result is that graphs of bounded
  VC dimension have (small) homogeneous vertex-partitions, i.e., partitions 
 where almost every pair of parts has density close to 0 or 1. Recently, Che
 rnikov and Towsner proved a hypergraph generalization of this fact. The qua
 ntitative aspects of their result remain open. I will present some recent p
 rogress on this problem, answering two questions of Terry. This is a joint 
 work with Asaf Shapira and Yuval Wigderson. </span></p>
DTSTAMP:20260830T051942
DTSTART;TZID=America/New_York:20251027T140000
DTEND;TZID=America/New_York:20251027T150000
SEQUENCE:0
TRANSP:OPAQUE
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