Title: Quantum matching problems
Speaker: Youming Qiao, UTS
Time/Location: 2-3pm, 16 March 2016 (Wed) / CB10.02.410, UTS
The first problem is the well-known polynomial identity testing problem, for which a deterministic efficient solution implies a strong arithmetic circuit lower bound. The second problem has a rich history and has appeared in various forms in a remarkable number of mathematical and computational areas. For example, it is a key problem in the theory of arithmetic circuits with divisions, as recently studied by Hrubeš and Wigderson. After introducing these problems, we will present a couple of ingredients in a recent deterministic efficient algorithm for the second problem. These include a polynomial degree upper bound on generating the ring of matrix semi-invariants, and a linear algebraic analogue of the augmenting path technique.