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.

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Month: April 2017

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

# Squaring the circle

# Spooky algebra II

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.

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

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