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SUMMARY:Combinatorics of Expanded Stable Maps - Cat Rust\, Queen Mary Univ
 ersity of London
DTSTART:20250606T133000Z
DTEND:20250606T143000Z
UID:TALK231241@talks.cam.ac.uk
CONTACT:Siao Chi Mok
DESCRIPTION:In logarithmic geometry\, one can consider moduli spaces of st
 able maps which satisfy some specified tangency conditions. One example is
  the moduli space M(x) of relative stable maps to P^1 which satisfy some r
 amification data x. We will begin with a result of Kannan on how invariant
 s of M(x) depend on x and then see how this can be generalised for maps to
  toric surfaces. We will then move on to introduce expanded stable maps\, 
 covering how to produce a map to a target expansion from a polyhedral subd
 ivision of a toric fan. Finally\, we will discuss how to tackle the analog
 ue of Kannan's result in this setting using tropicalisation\, and if time 
 permits\, the results so far. Any necessary toric or tropical background w
 ill be explained!
LOCATION:MR2 (note venue and time change!)
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