AbstractA classical theorem due to Birkhoff states that on a real or a complex symplectic manifold a function near its Morse critical point can be transformed by formal symplectomorphism into a power series in the pairwise sums of squares of the local coordinates, called its "Birkhoff normal form". A result of Sjöstrand says that, given certain conditions, one can compute the eigenvalues of the...
Record: NoLevel: Graduate & UndergraduateLanguage: ChinesePrerequisiteDifferentials Geometry, Linear Algebra, TopologyAbstractThis course introduces the algorithms and philosophy of Computational Discrete Global Geometric Structures. There are six components in this course: 1) the mathematical theory of global geometric structures on smooth manifolds; 2) their discrete counterparts; 3) the algo...