Junho Peter Whang, Decidable Diophantine Problems on Character Varieties

(This is a part of Arithemetic Geometry Day in IBS-CCG.)

Character varieties of manifolds are basic objects in geometry and low-dimensional topology. We motivate the Diophantine study of their integral points. After discussing an effective finite generation theorem for integral points on SL₂-character varieties of surfaces, we present new decidability results for certain Diophantine problems on character varieties with other coefficient groups and manifolds.