Artin Approximation concerns the solutions of algebraic or analytic equations in power series rings. Artin's celebrated theorem asserts that if a system f(x,y) = 0 admits a formal solution y(x), then it also admits a convergent solution y'(x). This result has seen many applications and has meanwhile obtained a fixed place in the mathematical landscape.
Artin's proof is a very tricky combination of various reduction steps, but it just ensures the existence of one convergent solution. Later results of Ploski, Popescu, Spivakovsky, Grinberg, Kazhdan, Drinfeld and others aim at understanding the structure of the whole solution set nearby a given formal solution.
As such, one is confronted with studying the infinite dimensional variety formed by all solutions. The study of these kind of solutions sets appears in different situations : in the study of arc spaces as be proposed by Nash, in non-archimedean analytic geometry or in tropical geometry for instance.
The conference proposes to bring these different viewpoints together and to design a route map for further research and understanding. It addresses people from commutative algebra, algebraic and analytic geometry, differential geometry, complex analysis, and functional analysis. Also post-docs and graduate students are welcome -- they should be offered a panorama of fascinating problems to investigate.