Miniworkshop "On the geometry and physics of Poisson structures"

Talks by Cédric Oms, Alberto Ibort and Narciso Román Roy

Quan?

16/01/2024 a 12:00 fins a 17/01/2024 a 13:00 (Europe/Madrid / UTC100)

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Sala d'actes de la FME

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Planning

Jan 15, all day long: Working group on Equivariant Floer homology by Alberto Ibort, Eva Miranda and Cédric Oms.

Jan 16 at 12:00 - Cédric Oms (BCAM):

Title: "A gentle introduction to Floer homology for b-surfaces."

In the late 80Andreas Floer developed an infinite-dimensional analog of Morse homology to tackle the so-called Arnold conjecture. He proved that the lower bound on fixed points of Hamiltonian diffeomorphisms is bounded below by topological means, namely that the number of fixed points is at least equal to the minimal number of critical points of a Morse function.
In this talk, I will discuss this conjecture for b-symplectic surfaces. To do this, I will talk about a generalization of the so-called "desingularization" as was first introduced by Guillemin-Miranda-Weitsman.
This is joint work with Eva Miranda and Joaquim Bruguès.

 

Jan 17 at 12:00-13:00 - Alberto Ibort (UC3M):

Title: "Representations of groups, groupoids, and the imprimitivity theorem."

Jan 17 at 13:00-14:00 - Narciso Román Roy (UPC):

Title: ``Multisymplectic and Multicontact de Donder-Weyl Hamiltonian Formulations for Field Theories’’.

The de Donder-Weyl  formulation is a covariant description of Hamiltonian classical (first order) field theories.
A geometric framework for this formulation is presented;
first, for  conservative Hamiltonian theories, using the multisymplectic approach, 
and, second, for nonconservative  (or ``action-dependent´´) Hamiltonian field theories,
by doing an extension of the above one which  is based on a generalization of the contact structures,
and is known as the multicontact formulation.
Special attention is devoted to the case of singular theories and, in particular, 
to the Hamiltonian formalism associated with regular and singular Lagrangian systems.
References:
[1] J.F. Cariñena, M. Crampin, and L.A. Ibort, 
“On the multisymplectic formalism for first order field theories”, 
Diff. Geom. Appl. 1(4) (1991) 345–374.
[2] M. de León, J. Marín-Solano, and J.C. Marrero, “A Geometrical approach to Classical Field Theories: A constraint algorithm for singular theories”, 
Proc. New Develops. Dif. Geom., L. Tamassi, J. Szenthe
eds., Kluwer Acad. Press, (1996) 291–312.
[3] M. de León, J. Marín-Solano, J.C. Marrero, 
“The constraint algorithm in the jet formalism”, 
Diff. Geom. App. 6(3) (1996) 275–300.
[4] J. Gaset, X. Gràcia, M. Muñoz-Lecanda, X. Rivas, and N. Román-Roy, 
“A contact geometry framework for field theories with dissipation”, 
Ann. Phys. 414 (2020) 168092.

 

Discussion on Equivariant Floer homology and b-models in physics From 16h-19h.
Participants of the workshop:
Joaquim Brugués
Alberto Ibort
Alfonso Garmendia
Søren Dyhr
Xavier Gracia
Eva Miranda
Pablo Nicolás
Cédric Oms
Narciso Román
Jagna Wisniewska

 

 

The talks will take place at Sala d'Actes FME.

more info: https://geodys.upc.edu/en/activities/on-the-geometry-and-physics-of-poisson-structures