Seminari/Colloquia
Pagina 21
Date  Type  Start  End  Room  Speaker  From  Title 

25/10/22  Seminario  16:00  17:00  1201 Dal Passo  Roberto Feola  Università di Roma Tre  Long time NLS approximation for a quasilinear Kleingordon equation on large compact domains
We consider a class of KleinGordon equations with quasilinear, Hamiltonian and quadratic nonlinearities posed on a large box with periodic boundary conditions.
We discuss how the cubic NLS equation can be derived to describe, approximately, the evolution of slow modulations in time and space of a spatially and temporarily oscillating wave packet.
We show that the approximation is valid over a time scale which goes beyond the natural quadratic lifespan of solutions of cubic equations. We provide error estimates in Sobolev spaces.
The proof is based on a combination of normal form techniques and energy methods.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 
14/10/22  Seminario  16:00  17:00  1201 Dal Passo  "Symmetries of supergeometries related to nonholonomic superdistributions"
We extend the Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracketgenerating distributions on supermanifolds and their structure reductions. Several examples will be demonstrated, including distributions with at most simple Lie superalgebras as maximum symmetry.
The talk is based on joint works with Andrea Santi, Dennis The and Andreu Llabres.  
14/10/22  Seminario  14:30  15:30  1201 Dal Passo  "Moment polytopes of spherical varieties and applications to multiplicityfree Hamiltonian manifolds"
Spherical varieties are a generalization of toric, symmetric and flag varieties. They are also relevant in symplectic geometry, in particular in relation with multiplicityfree Hamiltonian manifolds. In this talk we will describe how the combinatorial structures arising in this theory can be used to characterize those multiplicityfree manifolds that admit a Kähler structure, in terms of their moment polytopes.
This is a joint work with Bart Van Steirteghem.  
11/10/22  Seminario  16:00  17:00  1201 Dal Passo  Gaetano Siciliano  University of Sao Paulo (IMEUSP, Brazil)  Critical points under the energy constraint
In the talk we discuss the existence of critical points for a family of
abstract and smooth functionals on Banach spaces under the energy constraint.
By means of the LjusternickSchnirelmann theory and the fibering method of Pohozaev
we show, under suitable assumptions, multiplicity results.
The abstract framework is then applied to some partial differential equations depending
on a parameter for which we obtain multiple solutions as well as some bifurcation results.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
05/10/22  Seminario  16:00  17:00  1201 Dal Passo  Detlev Buchholz  University of Goettingen  Proper condensates and long range order
The usual characterization of BoseEinstein condensates is based on spectral properties of oneparticle density matrices. (OnsagerPenrose criterion). The analysis of their specific properties, such as the occurrence of longrange order between particles and peaks in momentum space densities requires, however, the transition to the thermodynamic limit, where the oneparticle density matrices are no longer defined. In the present talk, we will explain a new criterion of "proper condensation" that allows us to establish the properties of bosonic systems occupying fixed bounded regions. Instead of going to the idealization of an infinite volume, one goes to the limit of arbitrarily large densities in the given region. The resulting concepts of regular and singular wave functions can then be used to study the properties of realistic finite bosonic systems, the occurrence of condensates, and their largedistance behavior, with a precise control of accuracy.

04/10/22  Seminario  16:00  17:00  1201 Dal Passo  Lei Zhang  University of Florida (US)  Nonsimple Blowup solutions of singular Liouville equations
The singular Liouville equation is a class of second order elliptic partial differential equations defined in two dimensional spaces:
$$Delta u+ H(x)e^{u}=4pi gamma delta_0 $$
where $H$ is a positive function, $gamma>1$ is a constant and $delta_0$ stands for a singular source placed at the origin. This deceptively simply looking equation has a rich background in geometry, topology and Physics. In particular it interprets the Nirenberg problem in conformal geometry and is the reduction of Toda systems in Lie Algebra, Algebraic Geometry and Gauge Theory. Even if we only focus on the analytical aspects of this equation, it has wonderful and surprising features that attract generations of top mathematicians. The structure of solutions is particular intriguing when $gamma$ is a positive integer. In this talk I will report recent joint works with D’Aprile and Wei that give answers to some important issues of this equation. I will report the most recent results and consequences that our results may lead to.
Note: 1) This seminar will be held in presence, although the speaker will be connected remotely via MS Teams. The MS Teams link might be provided upon request to the organizers. 2) This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006. 
30/09/22  Seminario  16:00  17:00  1201 Dal Passo  "Higherorder theory for highest weight modules: positive weightformulas, resolutions and characters for higher order Verma modules"
We introduce higher order Verma modules over a KacMoody algebra g (one may assume this to be sl_{n} throughout the talk, without sacrificing novelty). Using these, we present positive formulas  without cancellations  for the weights of arbitrary highest weight gmodules V. The key ingredient is that of "higher order holes" in the weights, which we introduce and explain.
 
30/09/22  Seminario  14:30  15:30  1201 Dal Passo  "Integrable triples in simple Lie algebras"
We define integrable triples in simple Lie algebras and classify them, up to equivalence. The classification is used to show that all (but few exceptions) classical affine Walgebras W(g,f ), where g is a simple Lie algebra and f a nilpotent element, admit an integrable hierarchy of biHamiltonian PDEs. This integrable hierarchy generalizes the DrinfeldSokolov hierarchy which is obtained when f is the sum of negative simple root vectors.
 
28/09/22  Seminario  16:00  17:00  1201 Dal Passo  Jean Dolbeaut  Université Paris Dauphine  PSL  Stability estimates in some classical functional inequalities
In some classical functional inequalities, optimal functions and optimal constants are known. The next question is to understand which distance to the set of the optimal functions is controlled by the deficit, that is, the difference of the two sides of the inequality written with the optimal constant. In 1991, an answer was given by Bianchi and Egnell in the case of a Sobolev inequality on the Euclidean space, using compactness methods. A major issue with the method is that the new constant is so far unknown. The purpose of this lecture is to review some examples of related functional inequalities in which one can at least give an estimate of the stability constant.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 
21/09/22  Seminario  16:15  17:45  1201 Dal Passo  Fausto Di Biase  Università  On the differentiation of integrals in measure spaces along filters
In 1936, R. de Possel observed that, in the general setting of a measure space with no metric structure, certain phenomena, relative to the differentiation of integrals, which are familiar in the Euclidean setting precisely because of the presence of a metric, are devoid of actual meaning.
In this work, in collaboration with Steven G. Krantz, we show that, in order to clarify these difficulties,it is useful to adopt the language of filters, which has been introduced by H. Cartan just a year after De Possel's contribution.

<< 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 >>