Algebra, singularities, number theory and applications

PI1: Sara Arias de Reyna
PI2: Francisco J. Castro Jiménez

Abstract: Our project comprises different areas of mathematics, namely D-module theory, singularities, representation theory and number theory. We propose a series of open problems at the frontier of mathematical knowledge, including questions of a theoretical as well as computational nature. These problems concern cohomology, quasi-free divisors and D-modules, combinatorics and resolution of algebroid surfaces, differential structures in positive characteristic, Kronecker coefficients and representation theory, representation theory of nilpotent Lie algebras, filiform Lie algebras, expontential sums, torsion of abelian varieties over number fields and numerical semigroups.