< i>Origamis (also known as square-tiled\n surfaces) arise natura lly in a variety of settings in\n low-dimensional topology. They c an be thought of as surfaces\n obtained by gluing the sides of a co llection of unit squares.\n As such\, they generalise the torus whi ch can be obtained by\n gluing the sides of a single square. An or igami is said to be\n primitive if it is not a cover of a lo wer genus\n origami.\n
\n\n In this talk\, I will describe how one can define an action of\n the matrix group \\(\\mathrm{SL}(2\,\\mathbb{Z})\\) on primitive origamis. In\n ge nus two (with one singularity)\, the orbits of this action\n were c lassified by Hubert-Lelièvre and McMullen. By\n considering a gen erating set of size two for \\(\\mathrm{SL}(2\,\\mathbb{Z})\\)\,\n we can turn these orbits into an infinite family of\n four-valent g raphs. For a specific generating set\, I will\n explain how all bu t two of these graphs are non-planar. I\n will also discuss why th is gives indirect evidence for\n McMullen's conjecture that these g raphs form a family of\n expanders.\n
\n\n This is joint work with Carlos Matheus.\n
\n LOCATION:https://researchseminars.org/talk/GaTO/54/ END:VEVENT END:VCALENDAR