Related papers: The spectral curve of a quaternionic holomorphic l…
The Gauss map of a generic immersion of a smooth, oriented surface into $\mathbb R^4$ is an immersion. But this map takes values on the Grassmanian of oriented 2-planes in $\mathbb R^4$. Since this manifold has a structure of a product of…
We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the…
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…
We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit…
We study the self-adjointness of the two-dimensional Dirac operator coupled with electrostatic and Lorentz scalar shell interactions of constant strength $\varepsilon$ and $\mu$ supported on a closed Lipschitz curve. Namely, we present…
We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we…
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is…
This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov-Bohm solenoids in Euclidean three-space, the flux…
This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…
This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic…
We define a new topological polynomial extending the Bollobas-Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behavior under partial duality. This allows to write down a completely…
Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite…
Submanifolds in Lorentz-Minkowski space are investigated from various mathematical viewpoints and are of interest also in relativity theory. We define the hyperbolic surface and the de Sitter surface of a curve in the spacelike hypersurface…
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…
Adding a small subdominant quadratic in momentum term to a dominant linear Dirac dispersion curve affects conduction and valence band differently and leads to an hourglass-like structure for energy as a function of momentum. This applies to…
The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter…
This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that…
In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of…
A basic arbitrariness in the determination of the topology of a manifold at the Planck length is discussed. An explicit example is given of a `smooth' change in topology from the 2-sphere to the 2-torus through a sequence of noncommuting…