105 citations · 249 across the 12 of their papers we have counts for
4 papers · 1 filter
Moduli spaces of complex affine and dilation surfaces
Paul Apisa, Matt Bainbridge, Jane Wang
We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points…
Haupt's theorem for strata of abelian differentials
Matt Bainbridge, Chris Johnson, Chris Judge +1
Let S be a closed topological surface. Haupt's theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be re…
Billiards in L-shaped tables with barriers
Matt Bainbridge
We compute the volumes of the eigenform loci in the moduli space of genus two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in…
Euler characteristics of Teichmüller curves in genus two
Matt Bainbridge
We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single…