×Time: 14.15 on 23 Feb, 2023

Place: SR 05.002, Spiegelgasse 5

**Claire Burrin** (University of Zurich)

*Discrete lattice orbits in the plane*

I will discuss the following variant of the Gauss circle problem. Consider an orbit Gv, where G is a discrete group of invertible matrices and v is a vector in the plane. Under certain conditions (which can be made explicit) this orbit is discrete. How is this discrete set distributed in the plane? I will describe interesting features of such sets, and explain what makes them amenable to a mix of tools from number theory and harmonic analysis. My main goal will be to discuss a recent result with Samantha Fairchild on the 'weak uniform discreteness' of these sets.