Prof. David Krejčiřík z KM bude ve čtvrtek 5. ledna 2023 přednášet v AV ČR

Prof. David Krejčiřík z Katedry matematiky (KM) bude mít ve čtvrtek 5. ledna 2023 od 11:00 přednášku Is the optimal rectangle a square? Proběhne v sále 205 v hlavní budovy Akademie věd České republiky na Národní 3. Zhruba hodinová přednáška, která bude v anglickém jazyce, je přístupná všem zájemcům.

Abstract:

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.