Título: Models of mosquito population control strategies for fighting against arboviruses
Palestrante: Michel Duprez (Inria, Université de Strasbourg, ICUBE)
Data: 30/11/2022
Horário: 12:00h
Local: Sala C-116
Resumo: In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, a technique consist in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique). This talk is devoted to studying the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing the dynamic of a mosquitoes population, we will study the control problem and introduce the cost function standing for sterile insect technique. In a second step, we will consider a model with several patchs modeling the spatial repartition of the population. Then, we will establish some properties of these two optimal control problems. Finally, we will illustrate our results with numerical simulations.
Título: Rapid stabilization of linearized water waves and Fredholm backstepping for critical operators
Data: 29/11/2022
Horário: 14:00h
Local: Sala C-119
Palestrante: Ludovick Gagnon (Université de Lorraine, CNRS, Inria équipe SPHINX)
Resumo: The backstepping method has become a popular way to design feedback laws for the rapid stabilization of a large class of PDEs. This method essentially reduces the proof of exponential stability to the existence and invertibility of a transformation. Initially applied with a Volterra transformation, the Fredholm alternative, introduced by Coron and Lü, allows to overcome some existence issues for the Volterra transformation. This new approach also has the advantage of having a systematic methodology, but the methods known until now were only applicable to differential operators D_x^a with a>3/2. In this talk, we present the duality/compactness method to surmount this threshold and show that the Fredholm-type backstepping method applies for anti-adjoint operators i |D_x|^a, with a >1. We will demonstrate the application of this result for the rapid stabilization of the linearized water waves equation.
Título: Magic Functions
Palestrante: Felipe Gonçalves (IMPA)
Data: 19/10/2022
Horário: 12:00h
Local: Sala C-116
Resumo: We will talk about some of the challenging problems in different areas of mathematics that were solved by constructing certain "magic" functions with constraints on physical and/or frequency space (we shall focus slightly on the bandlimited case). The talk will be based entirely on examples, one of which is the sphere packing problem (its solution awarded the Fields medal to the Ukrainian female mathematician M. Viazovska).
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Palestra: A Hessian-dependent functional with free boundaries and applications to mean-field games
Palestrante: Julio C. Correa-Hoyos - UERJ
Data: 28/09/2022
Horário: 12h00
Local: Sala C-116
