Related papers: A point-plane incidence theorem in matrix rings
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new…
We consider an incidence problem in $\mathbb{R}^4$ which asks, for a set of $L$ lines and a set of $S$ planes in general position, what the maximum number of line-plane incidences is. A line-plane incidence is defined as a point where a…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
Let k be a regular F_p-algebra, let A = k[x,y]/(xy) be the coordinate ring of the coordinate axes in the affine k-plane, and let I = (x,y) be the ideal that defines the intersection point. We evaluate the relative K-groups K_q(A,I) in terms…
The Matrix Theory that has been proposed for various pp wave backgrounds is discussed. Particular emphasis is on the existence of novel nontrivial supersymmetric solutions of the Matrix Theory. These correspond to branes of various shapes…
We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
We show that the cohomology ring of Hilbert scheme of $n$-points in the affine plane is isomorphic to the coordinate ring of $\mathbb{G}_{m}$-fixed point scheme of the $n$-th symmetric product of $\mathbb{C}^{2}$ for a natural…
We study P\'olya urns on hypergraphs and prove that, when the incidence matrix of the hypergraph is injective, there exists a point $v=v(H)$ such that the random process converges to $v$ almost surely. We also provide a partial result when…
Our main result is the analysis of singularities of integrands of integrals representing matrix elements of scattering matrix and inclusive scattering matrix in perturbation theory. These results are proven for any quantum field theory in…
The surface states of intrinsic higher order topological phases are protected by the spatial symmetries of a finite sample. This property makes the existing scattering theory of topological invariants inapplicable because the scattering…
We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the…
We prove Pach-Sharir type incidence theorems for a class of curves in R^n and surfaces in R^3, which we call pseudoflats. In particular, our results apply to a wide class of generic irreducible real algebraic sets of bounded degree.
We propose a generalization of Heisenbergs' matrix mechanics based on many-index objects. It is shown that there exists a solution describing a harmonic oscillator and many-index objects lead to a generalization of spin algebra.
We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.
We prove a Cayley-Bacharach-type theorem for points in projective space $\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This is made possible by new bounds on the growth of the Hilbert function of almost complete…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.