Related papers: Opers and the twisted Bogomolny equations
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
We give an algebraic geometric compactification of certain moduli spaces of semistable E-pairs in the sense of Yokogawa. In particular, we obtain a compactification of the moduli spaces of semistable Higgs pairs on a curve which were…
A Theorem due to Guillemin and Sternberg about geometric quantization of Hamiltonian actions of compact Lie groups $G$ on compact Kaehler manifolds says that the dimension of the $G$-invariant subspace is equal to the Riemann-Roch number of…
We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable…
The goal of this work is to study some aspects of the geometry of the first cover $\Sigma^1$ in the Drinfeld tower over $\mathbb{H}^d_K$ the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. It is a cyclic \'etale…
Moduli spaces of compact stable $n$-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the…
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…
In this article we characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the so-called Bekolle-Bonami condition in terms of the Berezin transform.
The aim of this work is to give a twistor presentation of recent results about bi-Hermitian metrics on compact complex surfaces with odd first Betti number.
By refining the volume estimate of Heintze and Karcher \cite{HK}, we obtain a sharp pinching estimate for the genus of a surface in $\mathbb S^{3}$, which involves an integral of the norm of its traceless second fundamental form. More…
We consider Riemann surfaces obtained from nodal curves with infinite cylinders in the place of nodal and marked points, and study the space of finite energy vortices defined on these surfaces. To compactify the space of vortices, we need…
Let $X=\mathbb{C}\times\Sigma$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $X$ with finite analytic energy. The spin bundle $S^+\to…
We describe the reduction from four to two dimensions of the SU(2) Donaldson-Witten theory and the dual twisted Seiberg-Witten theory, i.e. the Abelian topological field theory corresponding to the Seiberg--Witten monopole equations.
Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to…
Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These…
In this paper, we consider Weingarten curvature equations for $k$-convex hypersurfaces with $n<2k$ in a warped product manifold $\overline{M}=I\times_{\lambda}M$. Based on the conjecture proposed by Ren-Wang in \cite{Ren2}, which is valid…
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first…
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric…
We consider the exotic vortex equations on compact Riemann surfaces. These generalise the well-known Jackiw-Pi and Ambj{\o}rn-Olesen vortex equations and arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in…
For a polarized family of complex projective manifolds, we identify the algebraic obstructions that govern the existence of approximate solutions to the Wess-Zumino-Witten equation. When this is specialized to the fibration associated with…