Related papers: Real Slices of Parabolic $\mathrm{SL}(r,\mathbb{C}…

An odd deformation of a super Riemann surface $\mathcal S$ is a deformation of $\mathcal S$ by variables of odd parity. In this article we study the obstruction theory of these odd deformations $\mathcal X$ of $\mathcal S$. We view…

With each antiholomorphic involution $\sigma $ of a connected complex semisimple Lie group $G$ we associate an automorphism $\epsilon_\sigma$ of the Dynkin diagram. The definition of $\epsilon_\sigma$ is given in terms of the Satake diagram…

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…

We address the inverse problem for holomorphic germs of a tangent-to-identity mapping of the complex line near a fixed point. We provide a preferred (family of) parabolic map $\Delta$ realizing a given Birkhoff--{\'E}calle-Voronin modulus…

We show that for any fixed point P on a Riemann surface S the distinct realizations of cocycles in H^1(S,O) correspond to the natural appearence of the standard Heisenberg vertex operator algebra II(P) and to the commutative Heisenberg…

Roe's partitioned manifold index theorem applies when a complete Riemannian manifold $M$ is cut into two pieces along a compact hypersurface $N$. It states that a version of the index of a Dirac operator on $M$ localized to $N$ equals the…

Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…

In the past few years, the theory of slice monogenic functions has been developed rapidly mainly motivated by the applications to an elegant functional calculus for non-commuting operators. In this article, we introduce the Teodorescu…

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…

Let $Mod_{g}$ be the modular group of surfaces of genus $g$. Each element $[h]\in Mod_{g}$ induces in the integer homology of a surface of genus $g$ a symplectic automorphism $H([h])$ and Poincar\'{e} shown that $H:Mod_{g}\to…

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…

We consider a manifold X obtained by a Kahler reduction of C^n, and we define its hyperkahler analogue M as a hyperkahler reduction of T^*C^n = H^n by the same group. In the case where the group is abelian and X is a smooth toric variety, M…

We consider differential operators $L$ acting on functions on a Riemannian surface, $\Sigma$, of the form $$L = \Delta + V -a K ,$$where $\Delta$ is the Laplacian of $\Sigma$, $K$ is the Gaussian curvature, $a$ is a positive constant and $V…

We study parabolic operators H = $\partial$t -- div $\lambda$,x A(x, t)$\nabla$ $\lambda$,x in the parabolic upper half space R n+2 + = {($\lambda$, x, t) : $\lambda$ > 0}. We assume that the coefficients are real, bounded, measurable,…

In this paper we study the completely bounded anti-isomorphisms on operator algebras, that work similarly to the involutions with the exception for the property of being completely isometric. We elaborate the Blecher's characterization…

In this paper we describe the fixed locus of a symplectic involution on a hyperk\"ahler manifold of type $K3^{[n]}$ or of Kummer $n$ type. We prove that the fixed locus consists of finitely many copies of Hilbert schemes of $K3$ surfaces of…

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces…

Given a real hyperelliptic algebraic curve $X$ with non-empty real part and a real effective divisor $\mc{D}$ arising via pullback from $\mathbb{P}^1$ under the hyperelliptic structure map, we study the real inflection points of the…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…