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Seminari 13 gennaio

Il giorno Lunedì 13 Gennaio

si terranno in Aula Rappresentanza i seguenti due seminari:


ore 14:00


Diego Catalano Ferraioli
(Universidade Federal de Salvador de Bahia)

The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors

Abstract
We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the twodimensional
Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a
fundamental set of first-order scalar differential invariants suitable for solution of the equivalence
problem. Genericity means that the Killing leaves are not null, the metric is not orthogonally
transitive (i.e., the distribution orthogonal to the Killing leaves is non-integrable), and two explicitly
constructed scalar invariants Cρ and ℓC are nonzero. All the invariants are designed to have
tractable coordinate expressions. Assuming the existence of two functionally independent
invariants, we solve the equivalence problem in two ways. As an example, we invariantly
characterize the Van den Bergh metric. To understand the non-generic cases, we also find all Λ-
vacuum metrics that are generic in the above sense, except that either Cρ or ℓC is zero. In this way
we extend the Kundu class to Λ-vacuum metrics. The results of the paper can be exploited for
invariant characterization of classes of metrics and for extension of the set of known solutions of the
Einstein equations. (Based on joint work with M. Marvan)

 


ore 15:00


Giorgio Gubbiotti
(University of Sidney)

Lagrangians and integrability of difference equations

Abstract
We present a recently found algorithmic method to solve the
inverse problem of the calculus of variations for scalar difference
equations of order higher than 2. We show how this algorithm can be
used to classify families of difference equations and study their
integrability properties.

 

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13 gennaio 2020
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