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SUMMARY:The diameter of the symmetric group: ideas and tools - Harald Helf
 gott (Université Paris 7 - Denis-Diderot\; Georg-August-Universität Göt
 tingen)
DTSTART:20170511T133000Z
DTEND:20170511T143000Z
UID:TALK72499@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Given a finite group <img alt="" src="http://www-old.new
 ton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0047.p
 ng">   and a set <img alt="" src="http://www-old.newton.ac.uk/js/MathJax/c
 urrent/fonts/HTML-CSS/TeX/png/Math/Italic/141/0041.png">   of generators\,
  the diameter <span><span><img alt="" src="http://www-old.newton.ac.uk/js/
 MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0064.png"><img alt
 ="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX
 /png/Main/Regular/141/0069.png"><img alt="" src="http://www-old.newton.ac.
 uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0061.png"><i
 mg alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-C
 SS/TeX/png/Main/Regular/141/006D.png"></span><img alt="" src="http://www-o
 ld.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141
 /0028.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current
 /fonts/HTML-CSS/TeX/png/Main/Regular/141/0393.png"><img alt="" src="http:/
 /www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regul
 ar/141/0028.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/c
 urrent/fonts/HTML-CSS/TeX/png/Math/Italic/141/0047.png"><img alt="" src="h
 ttp://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/
 Regular/141/002C.png"><img alt="" src="http://www-old.newton.ac.uk/js/Math
 Jax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0041.png"><img alt="" s
 rc="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/
 Main/Regular/141/0029.png"><img alt="" src="http://www-old.newton.ac.uk/js
 /MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0029.png"></span>
    of the Cayley graph <span><img alt="" src="http://www-old.newton.ac.uk/
 js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0393.png"><img 
 alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/
 TeX/png/Main/Regular/141/0028.png"><img alt="" src="http://www-old.newton.
 ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0047.png">
 <img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML
 -CSS/TeX/png/Main/Regular/141/002C.png"><img alt="" src="http://www-old.ne
 wton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0041.
 png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts
 /HTML-CSS/TeX/png/Main/Regular/141/0029.png"></span>   is the smallest <im
 g alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CS
 S/TeX/png/Main/Regular/141/2113.png">   such that every element of <img al
 t="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/Te
 X/png/Math/Italic/141/0047.png">   can be expressed as a word of length at
  most <img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/font
 s/HTML-CSS/TeX/png/Main/Regular/141/2113.png">   in <span><img alt="" src=
 "http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Mat
 h/Italic/141/0041.png"><img alt="" src="http://www-old.newton.ac.uk/js/Mat
 hJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/222A.png"><span><img 
 alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/
 TeX/png/Math/Italic/141/0041.png"><span>^(-<img alt="" src="http://www-old
 .newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/100/0
 031.png">)</span></span></span>  . We are concerned with bounding <span><s
 pan><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/
 HTML-CSS/TeX/png/Main/Regular/141/0064.png"><img alt="" src="http://www-ol
 d.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/
 0069.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/
 fonts/HTML-CSS/TeX/png/Main/Regular/141/0061.png"><img alt="" src="http://
 www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regula
 r/141/006D.png"></span><img alt="" src="http://www-old.newton.ac.uk/js/Mat
 hJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0028.png"><img alt=""
  src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/pn
 g/Math/Italic/141/0047.png"><img alt="" src="http://www-old.newton.ac.uk/j
 s/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0029.png"><span>
 <img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML
 -CSS/TeX/png/Main/Regular/141/003A.png"><img alt="" src="http://www-old.ne
 wton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/003D
 .png"></span><span><span><img alt="" src="http://www-old.newton.ac.uk/js/M
 athJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/006D.png"><img alt=
 "" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/
 png/Main/Regular/141/0061.png"><img alt="" src="http://www-old.newton.ac.u
 k/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0078.png"></s
 pan><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/
 HTML-CSS/TeX/png/Math/Italic/100/0041.png"></span><span><img alt="" src="h
 ttp://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/
 Regular/141/005C.png"><img alt="" src="http://www-old.newton.ac.uk/js/Math
 Jax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0064.png"><img alt="" 
 src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png
 /Main/Regular/141/0069.png"><img alt="" src="http://www-old.newton.ac.uk/j
 s/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0061.png"><img a
 lt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/T
 eX/png/Main/Regular/141/006D.png"></span><img alt="" src="http://www-old.n
 ewton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/002
 8.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fon
 ts/HTML-CSS/TeX/png/Main/Regular/141/0393.png"><img alt="" src="http://www
 -old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/1
 41/0028.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/curre
 nt/fonts/HTML-CSS/TeX/png/Math/Italic/141/0047.png"><img alt="" src="http:
 //www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regu
 lar/141/002C.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/
 current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0041.png"><img alt="" src="
 http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main
 /Regular/141/0029.png"><img alt="" src="http://www-old.newton.ac.uk/js/Mat
 hJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0029.png"></span>  . 
 <br></span><span><br>It has long been conjectured that the diameter of the
  symmetric group of degree <img alt="" src="http://www-old.newton.ac.uk/js
 /MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/006E.png">   is po
 lynomially bounded in <img alt="" src="http://www-old.newton.ac.uk/js/Math
 Jax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/006E.png">  . In 2011\,
  Helfgott and Seress gave a quasipolynomial bound (exp((log n)^(4+epsilon)
 )). We will discuss a recent\, much simplified version of the proof.&nbsp\
 ;</span>
LOCATION:Seminar Room 1\, Newton Institute
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