Related papers: Geometry and analysis of spin equations
We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…
We give a generalization of the nonexistence of level structures as Nadel, Noguchi, Hwang-To, for quasi-projective manifolds uniformized by strongly Carath\'eodory hyperbolic complex manifolds. Examples include moduli space of compact…
We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a…
For a k-flat F inside a locally compact CAT(0)-space X, we identify various conditions that ensure that F bounds a (k+1)-dimensional half flat in X. Our conditions are formulated in terms of the ultralimit of X. As applications, we obtain…
We construct a compactification of the moduli space of twisted holomorphic maps with varying complex structure and bounded energy. For a given compact symplectic manifold $X$ with a compatible complex structure and a Hamiltonian action of…
Let G be a p-adic reductive group, and R an algebraically closed field. Let us consider a smooth representation of G on an R-vector space V. Fix an open compact subgroup K of G and a smooth irreducible representation of K on a…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
In this review, we trace the evolution of the quantum spin-wave theory treating non-collinear spin configurations. Non-collinear spin configurations are consequences of the frustration created by competing interactions. They include simple…
One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the…
We establish the compactly generated shape (H-shape) index theory for local semiflows on complete metric spaces via more general shape index pairs, and define the H-shape cohomology index to develop the Morse equations. The main advantages…
We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a weighted projective space $\mathbb{WCP}_{[n_1,n_2]}^1$, often referred to as a spindle. Starting from the spindle solution of five-dimensional minimal…
We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…
We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional $\mathcal{N}=1$ supergravity coupled to a chiral non-linear sigma model and a Spin$^{c}_0$ structure. The model involves a…
We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to…
In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well…
We demonstrate new applications of the trace embedding lemma to the study of piecewise-linear surfaces and the detection of exotic phenomena in dimension four. We provide infinitely many pairs of homeomorphic 4-manifolds $W$ and $W'$…
In these proceedings we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model…
In this paper, we construct the supersymmetric spinning polynomials. These are orthogonal polynomials that serve as an expansion basis for the residue or discontinuity of four-point scattering amplitudes, respecting four-dimensional super…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…