In the 1950s, K. T. Chen introduced the iterated-integral signature of a piecewise continuously differentiable path. Up to a natural equivalence relation, this determines the initial path. In general, the signature of a path can be seen as a multidimensional time series. When the terminal time is fixed, the signature of a path can be seen as tensors and the calculation of the signature becomes a standard problem in data science. In this talk, I want to look at the signatures of paths from a combinatorial perspective in the shuffle algebra. We will discuss some recent results, also with an algebraic taste, and we will discuss an alternative proof of de Bruijn’s formula.
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15 May Friday
Laura Colmenarejo (UMass Amherst): Signatures of paths, the shuffle algebra, and de Bruijn’s formula
15 May 2020, 11:00 - 15 May 2020, 12:00
En ligne/online, Canada