Complex Analysis.
Mathematical Physics.
Differential Geometry.
Conformal and quasiconformal mappings.
Free boundary problems of fluid mechanics.
Teichmüller spaces.
Optimal control methods.
Main publications:
A.Vasil'ev: Moduli of families of curves for conformal and quasiconformal mappings. - ISBN 3-540-43846-7, Lecture Notes in Mathematics, vol. 1788, Springer-Verlag, Berlin- New York, 2002, 212 pp.
B.Gustafsson, A.Vasil'ev: Conformal and potential analysis in Hele-Shaw cells. - ISBN 3-7643-7703-8, Birkhduser Verlag, 2006, 231 pp.
B.Gustafsson, A.Vasil'ev: Analysis and Mathematical Physics. - ISBN: 978-3-7643-9905-4, Trends in Mathematics, Birkhäuser Verlag, 2009, 514 pp.
