Related papers: Isomorphism Problems of Noncommutative Deformation…

Fix $c\in (0,1)$ and let $\Gamma$ be a $\lfloor c n\rfloor$-regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency matrix $M$ of $\Gamma$ is invertible with high…

We elucidate the structure of D terms in N=1 orientifold compactifications with fluxes. As a case study, we consider a simple orbifold of the type-IIA theory with D6-branes at angles, O6-planes and general NSNS, RR and Scherk-Schwarz…

We investigate quantum corrections of the 2-d dilaton gravity near the singularity. Our motivation comes from a s-wave reduced cosmological solution which is classically singular in the scalar fields (dilaton and moduli). As result we find,…

In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations…

Let $B = \Bbbk_q[u,v]^{C_{n+1}}$ be a Type $\mathbb{A}_n$ quantum Kleinian singularity, which is an example of a noncommutative surface singularity. This singularity is known to have a noncommutative quasi-crepant resolution $\Lambda$,…

Let $G$ be a finite group and $M,N$ be two normal subgroups of $G$. Let $Aut_N^M(G)$ denote the group of all automorphisms of $G$ which fix $N$ element wise and act trivially on $G/M$. Let $n$ be a positive integer. In this article we have…

This note examines the geometry behind the Hamiltonian structure of isomonodromy deformations of connections on vector bundles over Riemann surfaces. The main point is that one should think of an open set of the moduli of pairs $(V,\nabla)$…

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical…

Two-dimensional (2d) $\mathcal{N}=(4,4)$ Lie superalgebras can be either "small" or "large", meaning their R-symmetry is either $\mathfrak{so}(4)$ or $\mathfrak{so}(4) \oplus \mathfrak{so}(4)$, respectively. Both cases admit a…

We say that a formal deformation from an algebra $N$ to algebra $A$ is strongly flat if for every real number $e $ there is a real number $0<s<e$ such that this deformation specialised at $t=s$ gives an algebra isomorphic to $A$. We show…

We investigate deformations of Milnor algebras of smooth homogeneous polynomials, and prove in particular that any smooth degree $d$ homogeneous polynomial in $n+1$ variables that is not of Sebastiani-Thom type is determined by the degree…

We study the existence of $L^2$ normalized solutions for nonlinear Schr\"odinger equations and systems. Under new Palais-Smale type conditions we develop new deformation arguments for the constraint functional on $S_m=\{ u; \,…

In this paper we study the algebra monomorphisms from A_m =R^(2^m) into A_n=R^(2^n) for 0<m<n where the A_k 's are the Cayley- Dickson algebras over the real numbers. We show that for m>2 there are many different types of monomorphisms and…

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…

We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…

For a noncompact complex hyperbolic space form of finite volume $X=\mathbb{B}^n/\Gamma$, we consider the problem of producing symmetric differentials vanishing at infinity on the Mumford compactification $\overline{X}$ of $X$ similar to the…

We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on the spaces of these two objects. The base field is taken to…

We prove a formula for the ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs $\mathcal{MG}_{g,n}$. Moreover, we prove that the rational ${\mathbb S}_n$-invariant cohomology of $\mathcal{MG}_{g,n}$ stabilizes for…