Many physical systems are described by partial differential equations
(PDEs). Determinism then requires the Cauchy problem to be well-posed.
Even when the Cauchy problem is well-posed for generic Cauchy data,
there may exist characteristic Cauchy data. Characteristics of PDEs play
an important role both in Mathematics and in Physics. In the first part
of the talk, I will review the theory of characteristics of PDEs, with a
special emphasis on intrinsic aspects, i.e., those aspects which are
invariant under general changes of coordinates. In the second part of
the talk, I will pass to a modern, geometric point of view, presenting
characteristics within the jet space approach to PDEs. In particular, I
will discuss the duality relation between characteristics and
singularities of solutions and observe that: "wave-fronts are
characteristic surfaces (and propagate along bicharacteristics)". This
remark may be understood as a mathematical formulation of the
wave/particle duality in optics and/or quantum mechanics.

Meeting ID: 814 591 7621 Passcode: 147983