Special Issue "Advances in singularities throughout Mathematics: Algebra, Topology, Geometry, Analysis, Number Theory, Combinatorics and Cryptography"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: closed (31 October 2019).
Interests: singularities; algebraic geometry; algebraic combinatorics; algebraic curves; topology of algebraic varieties; polytopes and lattice point counting
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
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- Singular varieties
- Singular maps
- Hodge structures
- Singular dynamical systems
- Theory of hyperplanes
- Toric varieties
- Real and complex singularities
- MS cryptography