While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization which advanced tools might bring new perspectives and approaches for this question. The first one is equivalence of satisfaction of 3-SAT problem with the question of...

Covariant first order differential calculus over quantum complex Grassmann manifolds is considered. It is shown by a Pusz–Woronowicz type argument that under restriction to calculi close to classical Kähler differentials there exist exactly two such calculi for the homogeneous coordinate ring. Complexification and localization procedures are used to induce covariant first order differential cal...

Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [1] and includes historical notes and b...

Each point x in Gr ( r , n ) corresponds to an × matrix A which gives rise a matroid M on its columns. Gel'fand, Goresky, MacPherson, and Serganova showed that the sets { y ? | = } form stratification of with many beautiful properties. However, results Mnëv Sturmfels show these strata can be quite complicated, particular may have arbitrary singularities. We study ideals I varieties, Zariski clo...