Searcharxiv⌕ Search

arXiv subjects

H. Hofer

Publications and source records attributed to H. Hofer.

3 recordsLinked to original sources
arXiv2005

Quantitative symplectic geometry

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between capacities often lead to surprising relations between different aspects of symplectic geometry and Hamiltonian dynamics. In this paper we present an attempt to better understand the space of all symplectic capacities, and discuss some further general properties of symplectic capacities. We also describe several new relations between certain symplectic capacities on ellipsoids and polydiscs. Throughout the discussion we mention many open problems.

math.SG↗
arXiv2003

Development of the Universe and New Cosmology

Cosmology is undergoing an explosive period of activity, fueled both by new, accurate astrophysical data and by innovative theoretical developments. Cosmological parameters such as the total density of the Universe and the rate of cosmological expansion are being precisely measured for the first time, and a consistent standard picture of the Universe is beginning to emerge. Recent developments in cosmology give rise the intriguing possibility that all structures in the Universe, from superclusters to planets, had a quantum-mechanical origin in its earliest moments. Furthermore, these ideas are not idle theorizing, but predictive, and subject to meaningful experimental test. We review the concordance model of the development of the Universe, as well as evidence for the observational revolution that this field is going through. This already provides us with important information on particle physics, which is inaccessible to accelerators.

astro-ph↗