Over the past few years, new methods have allowed singularists to achieve striking progress; among them we can cite the Floer homology, logarithmic geometry, the minimal model program, tropical geometry, perfectoid spaces. In the meantime new interactions have continued to emerge between singularity theory and other fields such as algebraic geometry, differential geometry, topology, dynamics, analysis and logic. Therefore singularity theory is currently a very active field which evolves very quickly and with fruitful achievements due to interactions between techniques from various horizons. The conference will be centered on the following 3 courses:

(1) A course about new methods in complex geometry coming from o-minimal geometry.

(2) A course on the recent proof, by J. Fernandez de Bobadilla and T. Pełka, of Zariski’s conjecture for μ-constant families.

(3) A course on foliation theory

Besides, 9 talks will take place during the conference; they will be about recent results in singularity theory. In particular, they will focus on complex geometry, the minimal model program, singularities in positive characteristic, and on metrics in singular spaces. Some of these talks will be given by young researchers and will allow them to present their works. The main goals of this program are the following ones:

– Bringing new collaborations, but also perpetuating current ones, between researchers working on problems related to singularity theory; as well as promoting transversal exchanges between different fields (topology, algebraic geometry, analysis, commutative algebra. . . ).

– Introducing new results in singularity theory, but also new tools that could be useful for singularists.

– Supporting PhD students and young researchers working in singularity theory or related fields.

– Bringing new research projects and promoting new collaborations.