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Lukas Gustafsson: Optimization in algebraic geometry and the EDD

Time: Fri 2020-05-15 13.00 - 14.00

Location: Zoom meeting ID 692 8571 8282

Participating: Lukas Gustafsson

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This seminar will be helt via Zoom, the meeting ID is 692 8571 8282


Finding critical points of a function subject to equality constraints is a classical optimization problem which in the general case is solved through the application of Lagrange multipliers. If the function and constraints are algebraic we may apply algebraic methods to the problem instead. An example of this is the Euclidean distance to a fixed point p, restricted to an algebraic variety. For a fixed variety, over the complex numbers, the number of such "distance"-critical points is constant for any choice of p (in some dense open​ subset of the ambient space). This is what is called the Euclidean Distance Degree (EDD). I will elaborate on the EDD and how these ideas might be applied within algebraic statistics.