Abstract:
Algebraic Complexity Theory studies the amount of resources required by algebraic algorithms for solving algebraic computational problems, such as multiplying matrices, computing determinants or applying the discrete Fourier transform.
Much like in the parallel universe of boolean computation, the basic problems in this area are widely open and we are very far from separating "algebraic P" from "algebraic NP" or from showing even modest limitations on the power of algebraic algorithms. In this talk I will describe some efforts from recent years towards the goal of proving lower bounds for strong algebraic computational models.
Based on several joint works with Abhranil Chatterjee, Prerona Chatterjee, Mrinal Kumar and Adrian She.