'Artin Approximation and Singularity Theory'
This semester has now ended
Further details can be found on the Chairholders' external website. It contains more pictures as well as a complete programme of all their activities - including those linked to the Thematic month that ran in February 2015. More information here.
Artin Approximation concerns the solvability of algebraic equations in spaces of formal, convergent or algebraic power series. The classical version asserts that if a formal solution exists, then there also exists a convergent, hence analytic, and even algebraic solution which approximates the formal solution up to any given degree. As such, the theorem is instrumental for numerous constructions in algebraic geometry, commutative algebra and recursion theory in combinatorics. A series is Nash or algebraic if it is algebraic over the polynomials. Nash series can be codified by polynomial data deduced from the minimal polynomial by the normalization of the respective algebraic hypersurface. This makes them computable. The field has seen renewed activity through the recent research on Arc Spaces, Motivic Integration and Infinite Dimensional Geometry. Important questions remain still unanswered (nested subring case, composition problems, structure theorems for the solution sets) and shall be investigated during the program. Fruitful interchanges with the singularity theory, the combinatorics and the algebraic geometry groups are expected. The scientific program is to be complemented by an exhibition series of algebraic surfaces in the city of Marseille, based on the very successful "Imaginary" program designed by Hauser for the Mathematisches Forschungsinstitut Oberwolfach.
Fakultät für Mathematik
Gallery of Singularities
Local Project Leader
I2M - Institut de Mathématiques de Marseille
Activities organized under the remit of the Chair at CIRM (Science)
Main conference: Artin Approximation and Infinite Dimensional Geometry
(1255) 23-27 March 2015
Doctoral school: Introduction to Artin Approximation and the Geometry of Power Series
(1254) 26-30 January 2015