Riemann surfaces in dynamics, topology and arithmetic

AMS Colloquium Lectures

1:00 pm, 19-21 January 2000, Washington DC

Curtis T. McMullen, Harvard University

Lectures slides:

I. The hyperbolic Laplacian and the Mandelbrot set
II. The shape of moduli space
III. From dynamics on surfaces to rational points on curves

References:

The Mandelbrot set is universal
Hausdorff dimension and conformal dynamics II: Geometrically finite rational maps
The moduli space of Riemann surfaces is Kähler hyperbolic
From dynamics on surfaces to rational points on curves
The Heavenly Emporium of Benevolent Knowledge

Illustrations:

Mandelbrot set blowup
Newton's method bifurcations
The Bers embedding of Teichmüller space