Quasiconformal mappings are generalizations of conformal
mappings. There are 3 main definitions of quasiconformality: metric,
geometric and analytic one. Their equivalence is known in various metric
measure space settings. However, until recent work by Ackermann (2010)
and Gartland, Jung, and Romney (2016), modern theory was unable to cover
the case of the Grushin plane. The talk will start with basic
definitions of quasiconformality in Euclidean spaces and example of the
appearance of quasiregular mapping in Physics. We will proceed with
defining quasiconformal mappings in a more general sense, outline
general knowledge about the equivalence of definitions in metric measure
spaces, and finally, provide recent development of this theory on the
Grushin plane.

Meeting ID: 828 4242 2342
Passcode: 274475