Dear Colleagues,

The increasing amount of new material related to singularity theory from a broad perspective is an opportunity to approach mathematics from this transversal viewpoint. From group theory to differential geometry, from topology to cryptography, from algebraic geometry to number theory or analysis, elements and topics in singularity theory establish connections that are both surprising and enriching.

The purpose of this Special Issue is to give researchers an opportunity to present their achievements in a monograph that offers an overview of the different perspectives, techniques, and applications of the modern and classical theory of singularities.

Possible topics of this issue are related, but not restricted, to the following:

• Topology of singular varieties;
• Local vs. global invariants of singularities: Normal singularities, zeta functions, Poincaré and Hilbert-type series, multiplier ideals, D-modules and B-polynomials, etc.
• Theory of hyperplanes: Hyperplane arrangements, toric hyperplanes, modules of logarithmic derivations, Terao’s conjecture, etc.
• Singular dynamical systems, orbits, stability, periodic solutions, etc.
• Polynomial maps: Jacobian conjecture, Milnor fibrations, elliptic fibrations, etc.
• Motivic invariants: Grothendieck ring, space of arcs, Nash problem, etc.
• Singular maps in differential geometry: Classification, bifurcation theory, etc.
• Deformation theory;
• Real and complex structures: Hodge theory, plurigenera, formality, etc.
• Groups in singularity theory: Quasiprojective or Kähler groups, braid monodromy, quotient singularities, invariant theory, etc.
• Combinatorial aspects: Toric varieties, lattice point counting, etc.
• Cryptography: Toric and polynomial maps, multivariate systems, etc.

Prof. José Ignacio Cogolludo-Agustín
Guest Editor

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• Singular varieties
• Singular maps
• Hodge structures
• Singular dynamical systems
• Theory of hyperplanes
• Toric varieties
• Real and complex singularities
• MS cryptography