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UID:7b23e806dbb11714f594918888658cd7
CATEGORIES:Discrete Math
CREATED:20231019T083911
SUMMARY:Tight Bound and Structural Theorem for Joints 
LOCATION:Hill 705
DESCRIPTION:Abstract: The joints problem asks to determine the maximum number of joints
  N lines can form, where a joint in a d-dimensional space is a point on d l
 ines in linearly independent directions. Recently, we determined the maximu
 m exactly for k choose d-1 lines in d-dimensional space, namely k choose d.
  What is more important is that we are able to prove a structural result de
 termining all optimal configurations, and this is the first success of the 
 polynomial method in this direction. It turns out that our result implies a
  conjecture of Bollobás and Eccles as an immediate corollary regarding a ge
 neralization of the Kruskal–Katona theorem. In this talk, we will talk abou
 t the connection to that conjecture and also give a high-level overview of 
 the key ideas. \n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract</strong>:&nbsp;The joints problem asks to determine the
  maximum number of joints N lines can form, where a joint in a d-dimensiona
 l space is a point on d lines in linearly independent directions. Recently,
  we determined the maximum exactly for k choose d-1 lines in d-dimensional 
 space, namely k choose d. What is more important is that we are able to pro
 ve a structural result determining all optimal configurations, and this is 
 the first success of the polynomial method in this direction. It turns out 
 that our result implies a conjecture of Bollobás and Eccles as an immediate
  corollary regarding a generalization of the Kruskal–Katona theorem. In thi
 s talk, we will talk about the connection to that conjecture and also give 
 a high-level overview of the key ideas.&nbsp;</p>
CONTACT:    Speakers: Hung-Hsun Hans Yu (Princeton) and Ting-Wei Chao (CMU)
DTSTAMP:20260826T234235
DTSTART;TZID=America/New_York:20231023T140000
DTEND;TZID=America/New_York:20231023T150000
SEQUENCE:0
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