Related papers: Some recent developments in K\"ahler geometry and …
Consider a compact K\"ahler manifold which either admits an extremal K\"ahler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal K\"ahler metric in K\"ahler classes…
This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few unrecorded results and formulates a number…
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra…
Recent results obtained in experiments at the LHC in the field of rare $b$-hadron decays are reviewed in this contribution, with a focus on $b\to q\ell\ell$ processes. A general status is presented as well as recently completed…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
This is a survey on our recent works which reveal new relationships among deformation quantization, geometric quantization, Berezin-Toeplitz quantization and BV quantization on K\"ahler manifolds.
The installation of forward proton detectors at the LHC will provide the possibility to perform new high-precision measurements, opening a novel window on physics beyond the Standard Model. We review recent simulations and theoretical…
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
HyperK\"ahler spaces, including manifolds, orbifolds and conical singularities play an important role in superstring/$M$-theory and gauge theories as well as in differential and algebraic geometry. In this paper we provide hundreds of new…
This contribution follows the talk, given by F. Delduc at the conference SQS'2011 in Dubna, Russia (July 18-23, 2011). To a considerable extent it is a summary of known facts about the links between geometry and extended supersymmetry in…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.
We find for the unitary evolution of spin-1/2 systems that the "purely mathematical mixed state holonomy of Uhlmann limitedly agrees, in the case of evolution over geodesic spherical triangles, with the holonomy "in the experimental context…
We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler…
This paper reviews recent advances in the study or circumstellar masers and masers found toward supernova remnants. The review is organized by science focus area, including the astrophysics of extended stellar atmospheres, stellar mass-loss…
We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…
We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
The goal of this note is to give an introduction to locally conformally symplectic and K\"ahler geometry. In particular, Sections 1 and 3 aim to provide the reader with enough mathematical background to appreciate this kind of geometry. The…
We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade.