| Résume | In recent years, the polynomial method has proven a powerful tool in different areas of mathematics, including number theory, harmonic analysis, computer science and combinatorics. We will discuss some improvements of this method over Euclidean space, including a sharp polynomial partitioning theorem over arbitrary varieties and new estimates on the behaviour of the connected components of real algebraic sets. As an application of these results, we provide a general degree-sensitive incidence bound for families of algebraic varieties of arbitrary degree and dimension. |
