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Lecture Series by A Krutov-3

Wednesday, May 9, 2018 - 15:00 to 16:30
Seminar Room, School of Mathematical Sciences
Andrey Krutov
Independent University of Moscow
Infinite jet spaces

We will extend our construction of finite jet spaces $J^k(\pi)$ to the
case when k goes to infinity. This will allows as to consider the wider
class of symmetries (higher symmetries) of partial differential
equations. We will define the bi-complex of differential forms on the
infinite jet space $J^\infty(\pi)$. We will to formalize the language
that will allow us to find, classify, and use the conserved
currents associated with systems of differential equations. The currents
reflect the continuity properties and manifest the presence of conserved
integral values, or charges, for all solutions of the system at hand. In
this lecture we explain in precisely what sense the equivalence classes
of conserved currents are dual to the notion of nontrivial
proper infinitesimal symmetries for differential equations.

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