March 26, 2025 (Wednesday), 4:10 pm

Steve Trettel, University of San Francisco

What do 3-manifolds Look Like?

Thurston’s Geometrization Theorem, later proved by Perelman, describes 3-manifolds in terms of geometric building blocks. Each manifold decomposes into pieces modeled on one of just eight homogeneous 3-dimensional spaces, known as the Thurston geometries.

In this talk, we explore the question: ‘What does a 3-manifold look like?’ through the lens of geometrization. After discussing how one might compute the “inside view” one would see in such spaces, we will use software written in collaboration with Remi Coulon, Sabetta Matsumoto, and Henry Segerman to explore some manifolds built from the Thurston geometries. Finally, we will see how these geometric pieces can be fit together to form a picture of general 3-manifolds.