Mathematics Winter School 

25/02/2021, 17:00 — 17:15 —
Paulo Mourão, Mathematics PhD Student at Université de Genève

Imaginary time flow deformations of Laughlin states

Even though we can easily model the behaviour of a charged particle under the influence of a magnetic field, the problem quickly grows very complicated as soon as we start considering many particle systems, due to the electromagnetic interaction between them. A breakthrough was achieved in 1983 when Robert Laughlin proposed an ansatz for the ground state of simple two dimensional systems of charged particles under the influence of a uniform magnetic field. This was later proven to be an excellent approximation to the exact wavefunctions. In my Master's thesis, we used techniques of Kähler geometry, geometric quantization and imaginary time Hamiltonian flows to deform these systems and thus obtain possible Laughlin states on deformed geometries. With this talk, I hope to provide some insight into modern applications of abstract mathematics to theoretical physics.

See also

ApresentaçãoPauloMOurao.pdf