*Every -complex is homotopy equivalent* to (the realization of) a *simplicial complex.*

# Small rings

Any field that is finitely generated as a ring is a finite field.

# Outside in

Given a group , embed in a larger group such that any automorphism of is the restriction of an inner automorphism of .

# Too complex to be true but too symmetrical to be false

For , let be a complex domain and let . Let be a complex Brownian motion starting from . Set .

Suppose that there exists a conformal isomorphism such that . Set and define for

and .

Then and have the same distribution.

# Squaring the circle

Is there a bijection of the plane sending every circle to a square?

# Spooky algebra II

Exhibit a group , a set of generators for and a subgroup such that for all and yet is not normal in .

# It’s counting time

What is the number of idempotent functions ?