[CvGmt News] Seminars by M. Mazzucchelli and W. Cheng (18/5/2017)

[Alfonso Sorrentino]

Giovedi' 18 Maggio 2017
Dipartimento di Matematica (Univ. di Roma Tor Vergata)
Aula Dal Passo

- 14:30  Marco Mazzucchelli (ENS Lyon & CNRS)
Title: Minimal Boundaries in Tonelli Lagrangian Systems

(15:30 Coffee break)

- 16:00  Wei Cheng (Nanjing University)
Title: On the singular dynamics of weak KAM solutions


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Abstracts:

Marco Mazzucchelli
Title: Minimal Boundaries in Tonelli Lagrangian Systems

Abstract: In this talk, which is based on joint work with Luca Asselle and
Gabriele Benedetti, I will present a few recent results concerning action
minimizing periodic orbits of Tonelli Lagrangian systems on an orientable
closed surface. I will show that in every level of a suitable low energy
range there is a "minimal boundary": a global minimizer of the Lagrangian
action on the space of smooth boundaries of open sets of the surface.
Minimal boundaries satisfy an analogue of the celebrated graph theorem of
Mather: in the tangent bundle, the union of the supports of all lifted
minimal boundaries with a given energy projects injectively to the base. I
will also present some corollaries of these statements to the existence of
simple periodic orbits with low energy on non-orientable closed surfaces,
and to the existence of infinitely many closed geodesics on certain
Finsler 2-spheres.




Wei Cheng
Title: On the singular dynamics of weak KAM solutions

Abstract: Let $H$ be a Tonelli Hamiltonian. We consider the propagation of
singularities along  generalized characteristics by an intrinsic method.
We will show that, for a prescribed solution $u$ which has the
representation in the form of inf-convolution, the relevant precess of
sup-convolution determines the propagation of singulars and generalized
characteristics for singular initial data. This method leads to the global
result under mild Tonelli conditions. We will also discuss the application
of this methods to  the associated singular dynamics in both topological
and differential sense. This is based on joint work with Piermarco
Cannarsa and Albert Fathi.


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Viale della Ricerca Scientifica 1
00133 Rome (Italy)

Phone: +39 06 72594663
Fax:      +39 06 72594699
Email: sorrentino at mat.uniroma2.it