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SUMMARY:Sunrose Shrestha (Tufts University\, USA)
DTSTART:20200617T150000Z
DTEND:20200617T160000Z
DTSTAMP:20260423T023051Z
UID:DinAmicI/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DinAmicI/7/"
 >The topology and geometry of random square-tiled surfaces</a>\nby Sunrose
  Shrestha (Tufts University\, USA) as part of DinAmicI: Another Internet S
 eminar\n\n\nAbstract\nA square-tiled surface (STS) is a branched cover of 
 the standard square torus with branching over exactly one point. They are 
 concrete examples of translation surfaces which are an important class of 
 singular flat metrics on 2-manifolds with applications in Teichmüller the
 ory and polygonal billiards. In this talk we will consider a randomizing m
 odel for STSs based on permutation pairs and use it to compute the genus d
 istribution. We also study holonomy vectors (Euclidean displacement vector
 s between cone points) on a random STS. Holonomy vectors of translation su
 rfaces provide coordinates on the space of translation surfaces and their 
 enumeration up to a fixed length has been studied by various authors such 
 as Eskin and Masur. In this talk\, we obtain finer information about the s
 et of holonomy vectors\, Hol(S)\, of a random STS. In particular\, we will
  see how often Hol(S) contains the set of primitive integer vectors and fi
 nd how often these sets are exactly equal.\n\nZoom link: https://unipd.zoo
 m.us/j/92074073847?pwd=ZDd6Y28yUVowcjJNUFFRYU52WGtTdz09\n
LOCATION:https://researchseminars.org/talk/DinAmicI/7/
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