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