·
MATH 648K (Fall
2011)
·
The principle
of minimal action in geometry and dynamics
· Instructor: Vadim Kaloshin MATH 3111,
vadim.kaloshin@gmail.com, (301) 4055132. Course
Information
The course will be devoted to analysis
of various minimization procedures in geometry and Hamiltonian dynamical systems
and their deep relation. For example, dynamics of planar billiards in convex
domains is closely related to the famous Kac’s
question: Can you hear the shape of a drum? 1.
Convex
billiards. Laplace spectrum, Length spectrum. 2.
Maximization
of perimeter, Mather betafunction and alphafunctions. 3.
AubryMather theory for twist (2dimensional) maps. 4.
Weak KAM
and Mather theory for multidimensional Hamiltonian systems 5.
Hofer
geometry 6.
Symplectic geometry We focus the
first part of the class on the book of Siburg ``Principle of minimal action in geometry and dynamics’’, Lecture Notes in
Mathematics 1844 The second part of
the class is focused on the book of Polterovich
``The Geometry of the group of symplectic diffeomorphisms’’. Lectures: TTh, 11:0012:15 p.m., MTH
B0427 Office
hours: appointment. 











