Noncommutative Geometry
Speaker: Masoud Khalkhali (Western)
"NCG learning seminar: Isothermal Coordinates 1"
Time: 14:30
Room: MC 107
In this year's NCG learning seminar we plan to look at different topics of current interest to our group here at Western. We shall have regular weekly meetings on Wednesday afternoons. Exact time and place has yet to be fixed and will be announced after scheduling meeting next week. The first couple of lectures will be devoted to isothermal coordinates. Isothermal coordinates play an important role in conformal geometry of surfaces (both commutative and noncommutative), and in uniformization of Riemann surfaces. They also appear naturally in foliation theory (Godbillon-Vey invariant) and in the definition of entropy in the second law of thermodynamics.
I shall first sketch a proof of their existence for general (analytic) Riemannian metrics and then discuss their relevance to other fields.