A SIR-type model with diffusion to describe the spatial spread of Covid-19

Speaker: Youcef Mammeri (Université de Picardie Jules Verne).

We all have to deal with the coronavirus epidemic. Many strategies have been put in place to try to contain the disease, with varying success. I will present an SIR-type mathematical model to predict the state of the epidemic. The effect of distancing, isolation of exposed individuals and treatment of symptoms will be compared. I will begin with a simple explanation of SIR models, then discuss a PDE model and its resolution.

Absence of positive eigenvalues of magnetic Schroedinger operators

Speaker: Hynek Kovařík (Università degli studi di Brescia).

Absence of positive eigenvalues of magnetic Schroedinger operators We study sufficient conditions for the absence of positive eigenvalues of magnetic Schroedinger operators in R^n. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field. A comparison with the examples of Miller-Simon shows that our result is sharp as far as the decay of the magnetic field is concerned.

Homogenization of Schrödinger equations. Extended Effective Mass Theorems for non-crystalline matter.

Speakers: Wladimir Neves (Universidade Federal do Rio de Janeiro).

In this talk, we study the homogenization of the Schrödinger equation beyond the periodic setting. More precisely, rigorous derivation of the effective mass theorems in solid state physics for non-crystalline materials are obtained.

This is a joint work with Vernny Ccajma and Jean Silva.

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