The occasion of Enrique Artal's and Alejandro Melle's birthday celebration, held in Jaca, Spain, on June 16-23, 2023, provided the backdrop for a gathering of world-renowned specialists, young researchers, and graduate students interested in singularity theory from the point of view of its multiple connections with the fields of topology, algebra, geometry, and number theory. This volume collects research papers and surveys from speakers and participants, together presenting a panorama of cutting-edge problems and cross-disciplinary approaches in the multifaceted interplay between topology and singularity theory with an eye toward presenting the state of the art in an accessible and approachable way. Specific topics include braid groups and braid monodromy, combinatorics and topology of hyperplane arrangements, embedded curves and surfaces, moduli space theory, Hodge index theory, and the study of arithmetic, topological, and algebraic invariants. This book is published in cooperation with Real Sociedad Matematica Espanola.
Jose Ignacio Cogolludo-Augustin, Universidad de Zaragoza, Spain. Eriko Hironaka, Florida State University, Tallahassee, FL
Articles; Maria Alberich-Carraminana, Josep Alvarez Montaner and Roger Gomez-Lopez, Multiplier ideals of meromorphic functions in dimension two; Patricio Almiron, On the rich landscape of complete intersection monomial curves; Enrique Artal Bartolo, Topology of complex plane curves: braid monodromy, local and global problems; Shinzo Bannai, Taketo Shirane and Hiro-o Tokunaga, Arithmetic of double covers and the topology of plane curves; S. Allen Broughton, Antonio F. Costa and Milagros Izquierdo, Modular companions in planar one-dimensional equisymmetric strata; Antonio Campillo and Raquel Melgar, Poincare series of semigroups; Jose I. Cogolludo-Agustin and Eva Elduque, Homotopy type of complements of fiber-type curves; Jose I. Cogolludo-Agustin, Tamas Laszlo, Jorge Martin-Morales and Andras Nemethi, Ordinary $r$-tuples in cyclic quotient surface singularities; Evelia R. Garcia Barroso, Pedro D. Gonzalez Perez and Patrick Popescu-Pampu, Lotuses as computational architectures; Benoit Guerville-Balle and Juan Viu-Sos, Connectedness and combinatorial interplay in the moduli space of line arrangements; A. Libgober, Alexander polynomials of elliptic configurations; Ignacio Luengo-Velasco, Alejandro Melle-Hernandez and Sabir M. Gusein-Zade, Power structures and their applications; Alexander I. Suciu, On the topology and combinatorics of decomposable arrangements; Andras Nemethi and Willem Veys, Filtrations associated with singularities; Jonathan Wahl, The volume of a surface or orbifold pair; Sebastian Xambo-Descamps, Discrete charms of Kahler geometry; Masahiko Yoshinaga, A construction of homotopically non-trivial embedded spheres for hyperplane arrangements
