Nonlinear differential equations on Fuchsian Triangle groups
TimeMay 31 2012 - 2:30pm - 3:30 pm
SpeakerSarbarish Chakravarty (University of Colorado, Colorado Springs)
We study a class of third order, nonlinear ordinary differential equations
whose solutions are described by certain types of Schwarz triangle functions.
These equations can be traced back to the work of Ramanujan, Chazy, Halphen and
many others, and their solutions are given in terms of Eisenstein series for the
modular group and its congruence subgroups. This talk will present our work in progress
toward a unified approach to derive such equations in a systematic fashion. We find
new equations whose automorphism groups are the arithmetic triangle groups classified
by Takeuchi. This is joint work with Mark Ablowitz (CU Boulder).