Handbook of Geometry and Topology of Singularities VI: Foliations

Felipe Cano Torres (PhD Universidad de Valladolid, Spain, 1983) is a researcher at Universidad de Valladolid. His research is on holomorphic foliations, particularly on reduction of singularities and applications to dynamical systems. Director of research of several international networks with European fundings. Co-founder and current subdirector of the CTRI, a center in Tordesillas, Spain, focusing on the relations between the University of Valladolid and Iberoamerica. José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.Lê Dũng Tráng (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975-1999) and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, and carousels, among other topics.José Seade (DPhil, University of Oxford 1980) is a researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research is in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor’s fibration theorem for analytic maps. He was awarded the 2021 Solomon Lefschetz Medal by the Mathematical Council of the Americas. He is currently President of the Mexican Academy of Sciences.

• 1 Adolfo Guillot, On the singularities of complete holomorphic vector fields in dimension two.- 2 Julio Rebelo and Helena Reis, Singularities of holomorphic vector fields in dimensions ≥ 3: results and problems.- 3 Alcides Lins Neto, Codimension one holomorphic Foliations.- 4 Maurıcio Correa, Analytic varieties invariant by holomorphic foliations and Pfaff systems.- 5 Felipe Cano and Beatriz Molina-Samper, Local Invariant Hypersurfaces for Singular Foliations.- 6 Isao Nakai, From the perspective of nonsolvable dynamics on (C, 0): Basics and Applications.- 7 Javier Ribon, Description of the Zariski-closure of a group of formal diffeomorphisms.- 8 Frank Loray, The Riemann-Hilbert correspondence for rank 2 meromorphic connections on curves.- 9 Emmanuel Paul, Jean-Pierre Ramis, Dynamics of the fifth Painlevé foliation.- 10 Jean-Pierre Ramis, Epilogue: Stokes phenomena. Dynamics, Classification Problems and Avatars.