Related papers: Dubrovin conjecture and the second structure conne…

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine…

Take a closed monotone symplectic manifold containing a smooth anticanonical divisor. The quantum connection on its cohomology has singularities at zero and infinity (in the quantum parameter). At zero it has a regular singular point, by…

We define a cohomology for an arbitrary $K$-linear semistrict semigroupal 2-category $(\mathfrak{C},\otimes)$ (called in the paper a Gray semigroup) and show that its first order (unitary) deformations, up to the suitable notion of…

This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate…

Inspired by the low wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, and by the realization that in Loop Quantum Gravity the holonomy of a flat connection…

Among the many important geometric properties of quantum state space are: transitivity of the group of symmetries of the cone of unnormalized states on its interior (homogeneity), identification of this cone with its dual cone of effects…

We explain how homotopical information of two composeable relations can be organized in two simplicial categories that augment the relations row and column complexes. We show that both of these categories realize to weakly equivalent…

We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call a {\em Kronecker web}. We describe two functors between Kronecker webs and…

We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus $g$ with $n$ marked points. A large part of these relations has a surprisingly simple form: the…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n--th tensor powers, where the quotients are given by symmetric group twisted Frobenius…

In the past two decades, extensive research has been conducted on the (co)homology of various models of random simplicial complexes. So far, it has always been examined merely as a list of groups. This paper expands upon this by describing…

We analyse in detail the language of partially non-abelian Deligne cohomology and of twisted differential K-theory, in order to describe the geometry of type II superstring backgrounds with D-branes. This description will also provide the…

We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of puzzles with specified border labels that can be created using a list of eight…

We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…

The notions of predictability and visibility are essential in the mathematical formulation of wave particle duality. The work of Jakob and Bergou [Phys. Rev. A 76, 052107] generalises these notions for higher-dimensional quantum systems,…

We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence…

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we…

We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain complex on each link diagram. Although the result has been…

We introduce a new notion of a curvature of a superconnection, different from the one obtained by a purely algebraic analogy with the curvature of a linear connection. The naturalness of this new notion of a curvature of a superconnection…