Related papers: Twisted determinants on higher genus Riemann surfa…
For a family of compact Riemann surfaces X_t of genus g>1 parametrized by the Schottky space S_g, we define a natural basis for the holomorphic n-differentials on X_t which varies holomorphically with t and generalizes the basis of…
For 1D Dirac operators Ly= i J y' + v y, where J is a diagonal 2x2 matrix with entrees 1,-1 and v(x) is an off-diagonal matrix with L^2 [0,\pi]-entrees P(x), Q(x) we characterize the class X of pi-periodic potentials v such that: (i) the…
We present the Laplace operator associated to a hyperbolic surface $\Gamma\setminus\mathbb{H}$ and a unitary representation of the fundamental group $\Gamma$, extending the previous definition for hyperbolic surfaces of finite area to those…
Using Liu's modular invariance method and its odd-dimensional extension by Han and Yu, we establish new Witten rigidity theorems for the generalized Witten genus of twisted Dirac operators on even-dimensional spin$^c$ manifolds and twisted…
Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin$^c$-complex under consideration is allowed to be further twisted by certain natural exterior…
We define a class of topological A-models on a collection of Riemann surfaces, whose boundaries are sewn together along the seams. The target spaces for the Riemann surfaces are the Grassmanians Gr_{m_i,n} with the common value of n, and…
There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are…
The moduli associated with boundaries in a Riemann surface are parametrized by the positions and strengths of electric charges. This suggests a method for summing over orientable Riemann surfaces with Dirichlet boundary conditions on the…
We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…
In this note we investigate the nonelliptic differential expression A=-div sgn grad on a rectangular domain in the plane. The seemingly simple problem to associate a selfadjoint operator with the differential expression A in an L^2 setting…
We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting factor"). If the twisting factor is fundamental…
We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a…
In this paper we applied the contour integral method for the zeta function associated with a differential operator to the Laplacian on a surface of revolution. Using the WKB expansion, we calculated the residues and values of the zeta…
On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$ in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$ perturbations…
We prove a determinantal formula and Pfaffian formulas that respectively describe the $K$-theoretic degeneracy loci classes for Grassmann bundles and for symplectic Grassmann and odd orthogonal bundles. The former generalizes…
Following on from previous work we derive the non-linear differential equations of more general correlators of U(1) twist fields in two-dimensional massive Dirac theory. Using the conserved charges of the double copy model equations…
The theta characteristics on a Riemann surface are permuted by the induced action of the automorphism group, with the orbit structure being important for the geometry of the curve and associated manifolds. We describe two new methods for…
We consider a combinatorial Laplace operator on a sequence of discrete graphs which approximates the m-dimensional torus when the discretization parameter tends to infinity. We establish a polyhomogeneous expansion of the resolvent trace…