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X-WR-CALNAME:[gt.go] - 'Rainbow matchings in groups' by Alp Muyesser
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DESCRIPTION:/Exposé en anglais/Talk in english/ \n\nA rainbow matching in a
 n edge-coloured graph is a matching whose edges all have different colours
 . Let G be a group of order n and consider an edge-coloured complete bipar
 tite graph\, whose parts are each a copy of the group G\, and the edge (x\
 , y) gets coloured by the group element xy. We call this graph the multipl
 ication table of G. For which groups G does the multiplication table of G 
 have a rainbow matching? This is an old question in combinatorial group th
 eory due to Hall and Paige\, with close connections to the study of Latin 
 squares. The problem has been resolved in 2009 with a proof relying on the
  classification of finite simple groups. In 2021\, a 'simpler' proof for l
 arge groups appeared\, this time using tools from analytic number theory. 
 We present a third resolution of this problem\, again only for large group
 s\, and using techniques from probabilistic combinatorics. The main advant
 age of our approach is that we are able to find rainbow matchings in rando
 m subgraphs of the multiplication table of G. This flexibility allows us t
 o settle numerous longstanding conjectures in this area. For example\, Eva
 ns asked for a characterisation of groups whose elements can be ordered so
  that the product of each consecutive pair of elements is distinct. Using 
 our results\, we are able to answer this question for large groups. In thi
 s talk\, we will give a gentle survey of this area. \n\nThis is joint work
  with Alexey Pokrovskiy. \n\n[Alp Muyesser] ( University College London ) 
 \n\n[ https://alpmuye.github.io/ | https://alpmuye.github.io/ ] \n\n\nRema
 rks / Remarques \n\nFind all the information of the working group on this 
 [ https://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT?userlang=en 
 | web page ] . \nRetrouvez toutes les informations du GT sur cette [ https
 ://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT | page web ] .
DTSTART;TZID=Europe/Paris:20220603T140000
DTEND;TZID=Europe/Paris:20220603T150000
LOCATION:https://webconf.u-bordeaux.fr/b/mar-ef4-zed
SEQUENCE:0
SUMMARY:[gt.go] - 'Rainbow matchings in groups' by Alp Muyesser
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