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The explicit isomorphism problem and its applications"

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Let A be an algebra over a field K which is given by a basis and a multiplication table of the basis elements. Furthermore, suppose that A is isomorphic to M_n(K), the algebra of nxn matrices with entries from K. The algorithmic task, known as the explicit isomorphism problem, is to compute an isomorphism between A and M_n(K). This problem comes from computational representation theory, but has various applications in many areas of computational mathematics: solving diophantine equations, finding generators for the group of rational points of an elliptic curves, parametrizing algebraic varieties. Recently, it has also been linked to the creation of error-correcting codes and cryptography. After surveying the known cases of the explicit isomorphism problem, I would like discuss these applications.

This talk is part of the Computer Security Seminars series.

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