Analysis, Applied Math and Geometry Seminar
Fall 2026
- Location: South Engineering 118
- Time: Tuesdays, 11:00-11:50 am
- Organizer: Maria Alfonseca-Cubero
15 September 2026
Stephanie Juntunen:
Floating bodies in equilibrium with variable densities
Abstract: In his 1822 memoir, Dupin established three fundamental laws for floating bodies. In the first talk, we will give a generalization these laws to the entire R^n with a probability density, and discuss their connection to Ulam’s Problem 19.
In the following talk, we will further explore probability densities with compact support and address a question similar to Ulam’s.
22 September 2026
Stephanie Juntunen:
Floating bodies in equilibrium with variable densities (Part 2)
29 September 2026
Reynold Fregoli:
Rational Approximations and Dynamics in the space of lattices
Abstract: Diophantine approximation asks how well real numbers can be approximated by rational numbers. A classical way to study this question is through continued fractions, but there is another point of view that connects it to dynamics on the space of lattices. In this talk, I will introduce this correspondence in its simplest setting. We will see how rational approximation to a real number can be encoded by short vectors in a lattice, and how the action of the diagonal flow translates Diophantine properties into geometric properties of trajectories.
This talk is intended as a gentle introduction to the subject, in preparation for my second talk next week.
6 October 2026
Reynold Fregoli