Related papers: Bubble divergences: sorting out topology from cell…
The homotopical information hidden in a supersymmetric structure is revealed by considering deformations of a configuration manifold. This is in sharp contrast to the usual standpoints such as Connes' programme where a geometrical structure…
For coupled-channel resonance scattering we derive a model with a closed form solution for the $T$-matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method…
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for…
Since the 1970s, it has been known that any open connected manifold of dimension 2, 4 or 6 admits a complex analytic structure whenever its tangent bundle admits a complex linear structure. For half a century, this has been conjectured to…
We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality…
In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…
We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring…
Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…
Cell extrusion is an essential mechanism for controlling cell density in epithelial tissues. Another essential element of epithelia is curvature, which is required to achieve complex shapes, like in the lung or intestine. Here we introduce…
We re-examine the problem of gauging the Wess-Zumino term of a d-dimensional bosonic sigma-model. We phrase this problem in terms of the equivariant cohomology of the target space and this allows for the homological analysis of the…
We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension 1 (i.e. a double fixed point) under conjugacy. These generic unfolding depend on one real parameter. The classification is done…
In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…
We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of $E_{1}$-degeneracy of the Hodge-de Rham spectral…
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $\Sigma$ that separates two subsystems of quantum strongly coupled…
The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of…
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…
We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of $\Gamma$-convergence theory, in two steps: firstly, we…