相关论文: Super volumes and KdV tau functions
The modular transformations of the $(1|1)$ complex supermanifolds in the like-Schottky modular parameterization are discussed. It is shown that these "supermodular" transformations depend on the spinor structure of the supermanifold by…
Via Andersen-Borot-Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur-Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's…
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of psi-classes supported on the boundary cycles of…
We review Mirzakhani's recursion for the volumes of moduli spaces of orientable surfaces, using a perspective that generalizes to non-orientable surfaces. The non-orientable version leads to divergences when the recursion is iterated, from…
We consider Novikov's Camassa-Holm type equation with cubic nonlinearity. In particular, we present a compact parametric representation of the smooth bright multisolution solutions on a constant background and investigate their structure.…
We formulate the Asymptotic Expansion Conjecture for the Witten-Reshetikhin-Turaev quantum invariants of closed oriented three manifolds. For finite order mapping tori, we study these quantum invariants via the geometric gauge theory…
We will describe algebro-geometric solutions of the KdV hierarchy whose $\tau$-functions in addition satisfy a generalization of the Virasoro constraints (and, in particular, a generalization of the string equation). We show that these…
We expand on the results of arXiv:1011.0780 where we presented new recursion relations for correlation functions of the stress tensor and conserved currents in conformal field theories with an AdS_p dual for p > 4. These recursion relations…
The moduli space of stable quotients introduced by Marian-Oprea-Pandharipande provides a natural compactification of the space of morphisms from nonsingular curves to a nonsingular projective variety and carries a natural virtual class. We…
In this article, following an insight of Kontsevich, we extend the famous Weil conjecture (as well as the strong form of the Tate conjecture) from the realm of algebraic geometry to the broad noncommutative setting of dg categories. As a…
In this paper, Peetre's conjecture about the real interpolation space of Besov space {\bf is solved completely } by using the classification of vertices of cuboids defined by {\bf wavelet coefficients and wavelet's grid structure}.…
We study the intersection theory of the $\Theta^{r,s}$-classes, where $r \geq 2$ and $1 \le s \le r-1$, which are cohomological field theories obtained as the top degrees of Chiodo classes. We show that the recently introduced generalized…
We consider algebras defined from quivers with relations that are k-th order derivations of a superpotential, generalizing results of Dubois-Violette to the quiver case. We give a construction compatible with Morita equivalence, and show…
We propose an explicit formula connecting Donaldson invariants and Seiberg-Witten invariants of a 4-manifold of simple type via Nekrasov's deformed partition function for the N=2 SUSY gauge theory with a single fundamental matter. This…
We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes,…
The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of non-stretching curves in Riemannian symmetric spaces G/SO(N). These spaces are…
We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement…
We generalise Mirzakhani's recursion to volumes of moduli spaces of bordered Klein surfaces, which include non-orientable surfaces. On these moduli spaces, the top form introduced by Norbury diverges as the lengths of 1-sided geodesics…
The classical Serre-Swan's theorem defines a bijective correspondence between vector bundles and finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these…
We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions,…