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Geometric complexity theory and matrix powering

2017
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Differential geometry and its applications
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Valiant's famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (Siam J Comput 2001, 2008) introduced geometric complexity theory, an approach to study this and related problems via algebraic geometry and representation theory. Their approach works by multiplying the permanent polynomial with a high power of a linear form (a process called padding) and then comparing the orbit closures of the determinant and the padded permanent.

doi:10.1016/j.difgeo.2017.07.001
fatcat:qqt6jaxvfraddcoqgqsvmxkndq