Speaker
Dr. Martin Schmoll, School of Mathematical and Statistical Sciences, Clemson’s University
Title
Mathematics Seminar Series
Subtitle
Counting Problems for Branched Solvable Translation Torus-Covers
Physical Location
Allen 14
Abstract:
We present results towards determining asymptotic quadratic growth rates for geodesic loops on solvable branched covers of flat tori. We start with some background on translation surfaces and recent results on generic cyclic covers obtained in collaboration with Aulicino, Calderon, Matheus and Salter. For generic cyclic covers we discovered a general formula that is surprisingly simple, it depends only on a few derived parameters. It does not depend, for example, on the actual number of branch points.
The essential features of that formula carry over to the broader more intricate class of solvable covers, at least for torus covers. We present a geometric path generalizing our results for generic cyclic (torus) covers.
Note:
Contact Shantia Yarahmadian or, syarahmadian@math.msstate.edu or (662) 325-7143 for additional information.