Inner geometry of complex surfaces: a valuative approach

no code implementations • 5 May 2019 • André Belotto da Silva, Lorenzo Fantini, Anne Pichon

We study the inner metric structure of the germ of an isolated complex surface singularity $(X, 0)$ by means of an infinite family of numerical analytic invariants, called inner rates.

Algebraic Geometry Primary 32S25, 57M27, Secondary 32S55, 14B05, 13A18

A general system of differential equations to model first order adaptive algorithms

no code implementations • 31 Oct 2018 • André Belotto da Silva, Maxime Gazeau

In this paper, we derive a non-autonomous system of differential equations, which is the continuous time limit of adaptive optimization methods.