##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Bradley Zykoski

#### University of Michigan

## Strongly Obtuse Rational Lattice Triangles

##### Abstract:

The dynamics of a billiard ball on a triangular table can be studied by considering geodesic trajectories on an associated singular flat metric structure called a translation surface when the angles of the triangle are commensurable with pi. In the case of the isosceles right triangle, this surface is a torus, whose geodesic trajectories in any direction are either all periodic or all uniquely ergodic. Triangles satisfying such a dichotomy are called lattice triangles, and our work contributes to the ongoing classification of such triangles. We make use of a number-theoretic criterion of Mirzakhani and Wright to classify such triangles with a large obtuse angle. This work is joint with Anne Larsen and Chaya Norton.

Host: Brandon Seward

### February 22, 2024

### 10:00 AM

Zoom ID 967 4109 3409

Research Areas

Ergodic Theory and Dynamical Systems****************************