BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Discrete Math/Algebra Seminar: Mutasim Mim\, Graduate Center\,
  CUNY
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260616T093027Z
UID:tag:localist.com\,2008:EventInstance_52619694887985
DTSTART:20260427T130000Z
DTEND:20260427T140000Z
DESCRIPTION:Title: When do triangles generate the cycle space in strongly r
 egular graphs?\n\nAbstract: We classify the strongly regular graphs for wh
 ich the first clique homology group can fail to vanish over some field. Us
 ing Neumaier's classification of strongly regular graphs with fixed smalle
 st integral eigenvalue\, together with vanishing results for the geometric
  and pseudogeometric families of graphs appearing there\, we prove that no
 n-vanishing $\\hlcl{G}{\\FF}$ can occur only in a short explicit collectio
 n of cases: the surviving graphs in Seidel's classification of strongly re
 gular graphs with smallest adjacency eigenvalue $-2$\, complete bipartite 
 graphs\, the conference graphs on at most $255$ vertices\, and the excepti
 onal families $E_m$ for some $m \\geq 3$ in Neumaier's classification. In 
 particular\, if $(G_n)_{n\\geq 1}$ is an infinite family of pairwise disti
 nct strongly regular graphs with $\\hlcl{G}{\\FF_n}\not=0$ for every $n$\,
  then either $G_n$ is a lattice graph for infinitely many $n$\, or $\\lim_
 {n\\rightarrow +\\infty} \\lambda_{\\min}(G_n)=-\\infty.$ Thus\, the latti
 ce graphs are the only surviving infinite family with bounded smallest eig
 envalue. For Latin square graphs\, we compute the remaining clique homolog
 ies completely: if $G$ is the strongly regular graph associated with a Lat
 in square $M$ of order $n \\geq 5$ and $\\FF$ any field\, then $H_i(\\clc{
 G}\,\\FF)=0$ for $i=1$ or $i \\geq 3$\, and $\\dim H_2(\\clc{G}\,\\FF)=(n-
 1)^3-I(M)\,$ where $I(M)$ is the number of $2 \\times 2$ sub-Latin squares
  in $M$.
GEO:39.681267;-75.754997
LOCATION:Ewing Hall\, 336
SUMMARY:Discrete Math/Algebra Seminar: Mutasim Mim\, Graduate Center\, CUNY
URL;VALUE=URI:https://events.udel.edu/event/discrete-mathalgebra-seminar-mu
 tasim-mim-ccny-cuny
CATEGORIES:Academics
CATEGORIES:College of Arts and Sciences
END:VEVENT
END:VCALENDAR