BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Lei Xue (University of Washington)
DTSTART:20220127T171500Z
DTEND:20220127T180000Z
DTSTAMP:20260424T094651Z
UID:CJCS/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/57/">A 
 Proof of Grünbaum’s Lower Bound Conjecture for polytopes\, lattices\, a
 nd strongly regular pseudomanifolds.</a>\nby Lei Xue (University of Washin
 gton) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\
 nIn 1967\, Grünbaum conjectured that any $d$-dimensional polytope with $d
  + s \\leq 2d$ vertices has at least $\\phi_k (d + s\, d) = {d + 1 \\choos
 e k + 1} + { d \\choose k + 1} - { d + 1 - s \\choose k + 1}$ $k$-faces. I
 n the talk\, we will prove this conjecture and discuss equality cases. We 
 will then extend our results to lattices with diamond property (the inequa
 lity part) and to strongly regular normal pseudomanifolds (the equality pa
 rt). We will also talk about recent results on $d$-dimensional polytopes w
 ith $2d + 1$ or $2d + 2$ vertices.\n
LOCATION:https://researchseminars.org/talk/CJCS/57/
END:VEVENT
END:VCALENDAR