Title:

The norther, the rounder

Abstract:

In 1877 Joel Asap Allen developed a rule stating that animals adapted to cold climates have shorter and thicker limbs and bodily appendages than animals adapted to warm climates. In this talk, we will explore how spectral geometry, and in particular Faber-Krahn inequality, can explain Allen's rule. Next, we will discuss other eigenvalue inequalities and how these inequalities change when we consider different boundary conditions or introduce a magnetic field.