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SUMMARY:Christoph Haase (UCL\, London)
DTSTART:20201110T181500Z
DTEND:20201110T184500Z
DTSTAMP:20260423T023010Z
UID:LA-CoCo/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LA-CoCo/17/"
 >On the size of finite rational matrix semigroups</a>\nby Christoph Haase 
 (UCL\, London) as part of LA Combinatorics and Complexity Seminar\n\n\nAbs
 tract\nGiven a finite set of $n \\times n$ integer matrices $\\mathcal M$ 
 that\ngenerate a finite multiplicative semigroup $\\overline{\\mathcal M}$
 \, I am\ngoing to present a recent result showing that any $M \\in\n\\over
 line{\\mathcal M}$ is a product of at most $2^{O(n^2 \\log n)}$\nelements 
 from $\\mathcal M$. This bound immediately implies a bound on\nthe cardina
 lity of $\\overline{\\mathcal M}$.\n\nI will provide a non-technical proof
  sketch demonstrating how the\naforementioned bound can be obtained. In ad
 dition\, I will discuss the\nhistory of this problem\, its motivation\, wh
 ich is rooted in automata\ntheory\, related results that have appeared ove
 r the last decades\, and\nopen challenges.\n\nThe talk is based on joint w
 ork with Georgina Bumpus\, Stefan Kiefer\,\nPaul-Ioan Stoienescu and Jonat
 han Tanner from Oxford\, which appeared at\nICALP'20\n
LOCATION:https://researchseminars.org/talk/LA-CoCo/17/
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