Jan 16 – 20, 2023
Europe/Paris timezone

David Krejcirik: Is the optimal rectangle a square?

Jan 16, 2023, 5:00 PM
Amphithéâtre Schwartz (IMT)

Amphithéâtre Schwartz


Université Paul Sabatier, 118 Route de Narbonne, 31000 Toulouse France


We give a light talk on an optimality of a square in geometry and physics. First, we recollect classical geometric results that the square has the largest area (respectively, the smallest perimeter) among all rectangles of a given perimeter (respectively, area). Second, we recall that the square drum has the lowest fundamental tone among all rectangular drums of a given area or perimeter and reinterpret the result in a quantum-mechanical language of nanostructures. As the main body of the talk, we present our recent attempts to prove the same property in relativistic quantum mechanics, where the mathematical model is a matrix-differential (Dirac) operator with complex (infinite-mass) boundary conditions. It is frustrating that such an illusively simple and expected result remains unproved and out of the reach of current mathematical tools.

Presentation materials

There are no materials yet.