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CRM > English > Activities > Curs 2019-2020 > IRP Dynamical Systems: Weekly joint seminar
IRP Dynamical Systems: Weekly joint seminar
Past sessions

February 24th, 2020
Room: CRM -  Auditori
Time: 15:30 (coffee break served at 15:15)

Title: Vortex and gravitational modelling on surfaces: Hodge’s decomposition theorem and the stability of a ring.
Speaker: Stefanella Boatto (Universidade Federal de Rio de Janeiro)

Abstract:
Vortex and gravitational dynamics have a long fascinating interwoven history, both for the modelling and for the different areas of mathematics needed to study the corresponding models. Philosophical questions reside behind the modelling part, as for example how do we define gravity beyond our Euclidean perception? Are the laws, we are so familiar with, universal ? What is the geometry of our universe? Helmoltz-Hodge’s decomposition for vector fields – known from courses of vector calculus – and its corresponding version for differential forms, known as Hodge’s decomposition theorem, help us in possible generalisation of incompressible fluids and gravitational dynamics on a large variety of surfaces and manifolds of higher dimensions.

For the fluid case the stability of a ring of vortices has attracted the interest of  researchers for over a century. Recent beautiful observations of polygonal configurations of vortices present in the atmospheres of Jupiter and Saturn, and of polygonal jets in the Earths atmosphere have revived the interest in the subject. In the observed cases the vortex ring is in the presence of a central vortex. I will present analytical and numerical results about the linear, spectral and Lyapunov stability of a ring in the presence of polar vortices. Motivated by both atmospheric observations we considered the special case of total vorticity equal to zero. Such a case has also the very nice property of being universal, i.e., to not depend on a choice of gauge. Joint work with Carles Simó.

For the N-body case, we explore how the geometry and the topology of the surface have and impact in the dynamics. Join work with Rodrigo Schaefer, Gladston Duarte, David Dritschel, Teresa Stuchi, Thierry Combot and Jaime Andrade.                                         

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March 2nd, 2020
Room: CRM -  Auditori
Time: 15:30 (coffee break served at 15:15)

Title: The Markus-Yamabe Conjecture for Continuous and Discontinuous Piecewise Linear Differential Systems 
Speaker: Jaume llibre, UAB 



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March 9th, 2020
Room: CRM -  Auditori
Time: 15:30 (coffee break served at 15:15)

Title: Global dynamics of the real secant method 
Speaker: Antonio Garijo (Universitat Rovira i Virgili)

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Title: On the proof of the 16th Hilbert problem.
Speaker: Jaume Llibre (Universitat Autònoma de Barcelona)

Room: CRM Auditorium

➤ Monday, February 10thfrom 15:00 to 17:00. *Coffee-break from 14:40 to 15:00. 
​➤ Tuesday, February ​11thfrom 9:00 to 11:00. *Coffee-break from 11:00 to 11:20.

​➤ Wednesday, February 12th, from 10:00 to 12:00.​ *Coffee-break from 9:40 to 10:00.

​➤ Thursday, February 13thfrom 11:00 to 13:00. *Coffee-break from 10:40 to 11:00


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