Charles Daly's Homepage

Thanks for stopping by! My name is Charles and I'm a Postdoctoral Scientist at the Max Planck Institute in the Geometry, Groups, and Dynamics group led by Anna Wienhard . Here you can find some of my research, teaching materials, and some math pictures.

My work is in low-dimensional topology and geometry with an emphasis on hyperbolic, affine, and projective manifolds. I like to use computers to explore these areas of mathematics both visually and computationally.

Geometry is full of really wild surprises, and being able to illustrate these phenomena is one of my favorite things to do. Apart from doing math, I love animals, music, video games, and cartoons. Feel free to contact me and chat it up about math!

Update: I am on the job market as of August 2026!

Contact Information

Work Address: Inselstraße 22, 04103 Leipzig, Germany
Office: A3 09
Email Address:

Mathematical Visualizations

Triangles forming part of a torus in hyperbolic geometry — Some triangles that are gluing together to give part of a torus from a hyperbolic once-punctured torus bundle. A bunch of the triangles are similar. This picture is seen from infinity in hyperbolic 3-space.

Symplectic tiling billiards played on a Euclidean tiling
and an almost Euclidean tiling — This is a dynamical system on two billiard tables that relies on parallelism instead of angle reflection. Here it is being played on a Euclidean tiling on the left, and a nearby non-Euclidean tiling.

An incomplete hyperbolic structure on the thrice-punctured sphere — Here's a picture of an incomplete hyperbolic structure on the thrice-punctured sphere. There are two ideal hyperbolic triangles that glue together to give the hyperbolic structure.