Related papers: Some recent developments in K\"ahler geometry and …
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\"ahler reduction; projective superspace; the generalized Legendre construction;…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
We construct metrics with the holonomy group SU(2) on the tangent bundles of weighted complex projective lines and give a geometric description of the moduli space of special Kahler metrics on a K3-surface in the neighborhood of the flat…
This paper summarizes the results in Integral Biomathics obtained to this moment and provides an outlook for future research in the field.
We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified K\"ahler classes, which extend the notions of constant scalar curvature and extremal representatives for usual K\"ahler classes. In…
This paper, the second of a series, deals with the function space of all smooth K\"ahler metrics in any given closed complex manifold $M$ in a fixed cohomology class. The previous result of the second author \cite{chen991} showed that the…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
Lattice simulations of hadronic structure are now reaching a level where they are able to not only complement, but also provide guidance to current and forthcoming experimental programmes at, e.g. Jefferson Lab, COMPASS/CERN and FAIR/GSI.…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
We present classical and recent results on K\"ahler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI…
In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…
The latest results on searches for supersymmetry, extra dimensions and exotic phenomena from the LEP collaborations are presented. No significant signal-like excess is observed in the data. The results are interpreted in various models and…
I review here the most recent results about the observation and the study of hadronic bound states that do not fit well in the standard quarkonium picture. Several new states have been observed in the last few years, at B-, tau-Factories…
We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.
We study isometric maps between Teichm\"uller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but…
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…