Related papers: The Chern class for $K_3$ and the cyclic quantum d…

In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern (and Segre) classes of all tautological bundles on it and compute the nef…

Consider a complex algebraic group $G$ acting on a smooth variety $M$ with finitely many orbits, and let $\Omega$ be an orbit. The following three invariants of $\Omega\subset M$ can be characterized axiomatically: (1) the equivariant…

A model of K-homology with coefficients in a mapping cone using the framework of the geometric cycles of Baum and Douglas is developed. In particular, this leads to a geometric realization of K-homology with coefficients in R/Z. In turn,…

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…

In this paper, we find rational zeta series with $\zeta(2n)$ in terms of $\zeta(2k+1)$ and $\beta(2k)$, the Dirichlet beta function. We then develop a certain family of generalized rational zeta series using the generalized Clausen function…

In this note, we revisit the $\Theta$-invariant as defined by R. Bott and the first author. The $\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop…

In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra $\mathfrak{g}$. This problem reduces to the classification of all Lie bialgebra structures on…

In this article, we consider regular projective arithmetic schemes in the context of Arakelov geometry, any of which is endowed with an action of the diagonalisable group scheme associated to a finite cyclic group and with an equivariant…

Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a classification scheme for these intricate orbits in terms of periodic orbits. The crucial insight is that for a given effective angular momentum $L$ and angle of…

We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.

We establish a maximal parabolic version of the Kazhdan-Lusztig conjecture \cite[Conjecture 5.10]{CKW} for the BGG category $\mathcal{O}_{k,\zeta}$ of $\mathfrak{q}(n)$-modules of "$\pm \zeta$-weights", where $k\leq n$ and…

We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…

The entanglement Chern number, the Chern number for the entanglement Hamiltonian, is used to charac- terize the Kane-Mele model, which is a typical model of the quantum spin Hall phase with the time reversal symmetry. We first obtain the…

We show a quantum version of Chern character homomorphism from the small quantum K-theory to the small quantum cohomology in the cases of projective spaces and incidence varieties, whose classical limit gives the classical Chern character…

We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds,…

I suggest two new unitarity tests for the quark charged current coupling constants which are $(sin \gamma/sin \alpha) = \zeta$, and $(sin 2\gamma)/(sin 2\alpha) = - ((1-\zeta cos \beta))/(cos \beta-\zeta)$ where $\zeta$ is a CKM parameter…

We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the…

We construct some examples of D=3, N=4 GW theory and N=5 superconformal Chern-Simons matter theory by using the covariantly constant curvature of a quaternionic-Kahler manifold to construct the symplectic 3-algebra in the theories.…

Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute the…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…