If X is a smooth variety, let T∗X be the cotangent bundle of X

A compact G-space is called a G-boundary in the sense of Furstenberg ([F1, F2]) if X is minimal and strongly proximal, or equivalently if X is the unique minimal G-invariant

Note: This examination consists of ten questions on one page. a) Considering two arbitrary vectors a and b in three-dimensional Cartesian space, how can the angle between

No calculators are to be used on this exam. Note: This examination consists of ten questions on one page. Give the first three terms only. a) What is an orthogonal matrix?

This is reflected in the fact, proved in [33], that in the asymptotically Euclidean case the scattering matrix is a Fourier integral operator associated to the

Let s be the additive group of all (1) The work of this author was supported at various stages by NSF Grant No. This support is gratefully acknowledged.. We are greatly

(Recall that an irreducible variety of dimension n and degree d spans a linear space of dimension at most n + d − 1 ([EH]).) Since X has the same degree and dimension as the

A reformulation of the G¨ ottsche-Yau-Zaslow formula gives the generating function on the number of genus g curves ([Go98], remark 2.6), and this reformulation has been verified

In [16] Hasegawa studied K¨ ahler structures on some classes of solvmanifolds which are not only the completely solvable type, and suggested a generalized ver- sion of