Survey of Some Recent Results in Algebraic Complexity

Algebraic complexity studies the complexity of computing polynomials by arithmetic circuits - i.e. circuits that use the arithmetic operations +,*. Arithmetic circuits form a very elegant model of computation in which the (analog of the) P vs. NP problem may be easier to tackle. In recent years algebraic complexity has gained a lot of interest and some breakthrough results were obtained. In this talk we shall mention those breakthrough results and discuss some of the recent developments. In particular we shall mention results regarding depth reduction, lower bounds and algorithms for polynomial identity testing.