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SUMMARY:Ashwin Sah (MIT)
DTSTART:20220324T151500Z
DTEND:20220324T170000Z
DTSTAMP:20260422T065641Z
UID:CJCS/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/64/">Hi
 gh-Girth Steiner Triple Systems</a>\nby Ashwin Sah (MIT) as part of Copenh
 agen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nWe prove a 1973 conjec
 ture due to Erdős on the existence of Steiner triple systems with arbitra
 rily high girth. Our proof builds on the method of iterative absorption fo
 r the existence of designs by Glock\, Kü​hn\, Lo\, and Osthus while inc
 orporating a "high girth triangle removal process". In particular\, we dev
 elop techniques to handle triangle-decompositions of polynomially sparse g
 raphs\, construct efficient high girth absorbers for Steiner triple system
 s\, and introduce a moments technique to understand the probability our ra
 ndom process includes certain configurations of triples. In this talk we w
 ill also give a high-level overview of iterative absorption. This work is 
 joint with Matthew Kwan\, Mehtaab Sawhney\, and Michael Simkin.\n
LOCATION:https://researchseminars.org/talk/CJCS/64/
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