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Polinomials, Toeplitz matrices and convolution

Polynomials furnish the most important and perhaps most neglected concept in pure and applied mathematics. Yet they appear whenever we have finite setting.
Indeed, we meet them in the construction of extension fields, as annihilating polynomials in linear algera and module theory, in Zarisky topology, in DSP and DIP, in interpolation and numerical analysis, in coding and cryptography, in combinatorial biology, etc etc
Their importance to applied math comes in large part due to the tri-partheid relations between coefficients, roots and power-sums.
This will be a talk about the connection between polynomial multiplication and Toeplitz matrix multiplication. This connection will link the binary world to the polynomial world.
A block versions of this connection will be applied to the study of convolutional codes.
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