Tags » Cohomology

An abstract ergodic theorem, and the Mackey-Zimmer theorem

The von Neumann ergodic theorem (the Hilbert space version of the mean ergodic theorem) asserts that if is a unitary operator on a Hilbert space , and is a vector in that Hilbert space, then one has… 2,315 more words

Expository

Hypersurfaces, 4-manifolds, and characteristic classes

In this post we’ll compute the (topological) cohomology of smooth projective (complex) hypersurfaces in . When the resulting complex surfaces give nice examples of 4-manifolds… 4,927 more words

Algebraic Geometry

The Mittag-Leffler problem and the Dolbeault isomorphism.

In this post, will mean a compact Riemann surface (without boundary).

Let us start by considering a form of theĀ Mittag-Leffler problem: Given a point , can we find a global meromorphic function such that and ? 512 more words

Riemann Surfaces