Title: Log-Noetherian functions

Abstract:

In the early eighties Khovanskii defined the class of Pfaffian functions and proved that they satisfy an analog of the Bezout theorem: an explicit upper bound for the number of solutions for systems of equations in terms of the degrees. He conjectured that similar bounds hold for the larger class of "Noetherian functions". I will discuss a proof of this conjecture for Noetherian functions and a larger class of "log-Noetherian" functions. Unlike Khovanskii’s original topological approach, this proof involves several ideas inspired by algebraic geometry and resolution of singularities.

I’ll also explain how the solution of Khovanskii’s conjecture leads to "effective o-minimality" of a large structure containing many functions of interest in algebraic and arithmetic geometry, in particular period maps for variations of Hodge structures.

Zoom: https://huji.zoom.us/j/84202575300?pwd=QXBvNjV0bDBWUmwxVkFIYXpzQ29RQT09