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Descriptive set theory and uncountable model theory
Descriptive set theory uncountable model theory
2015/9/25
In the early days of the development of model theory it was considered
natural and was certainly beneficial to assume that the theories under investigation
were in a countable language. The primary ...
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry.Symmetries may be due to the interaction topology ...
Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
Instantons Quivers Noncommutative Donaldson-Thomas Theory
2011/3/2
We construct noncommutative Donaldson{Thomas invariants associated with abelian orbifold
singularities by analysing the instanton contributions to a six-dimensional topological gauge
theory.
Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds are discussed. We relate the three flavours ring-heoretic Morita equivalen...
M-theory, the signature theorem, and geometric invariants
M-theory the signature theorem geometric invariants
2011/3/2
The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator.
Gauge theory in dimension $7$
calibrations elliptic boundary problems on manifolds G2–manifolds
2011/3/1
We first review the notion of a G2–manifold, defined in terms of a principal G2 (“gauge”)
bundle over a 7–dimensional manifold, before discussing their relation to supergravity. In a
second thread, ...
On uniqueness of semi-wavefronts (Diekmann-Kaper theory of a nonlinear convolution equation re-visited)
semi-wavefronts Diekmann-Kaper theory
2010/11/22
Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kape...
Many different programs are the implementation of the same algorithm. This makes the collection of algorithms a quotient of the collection of programs. Similarly, there are many different algorithms ...
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show i...
Abelian Yang-Mills theory on Real tori and Theta divisors of Klein surfaces
Abelian Yang-Mills theory Real tori Theta divisors
2010/11/11
The purpose of this paper is to determine natural theta line bundles of Klein surfaces as elements in the Grothendieck cohomology group which classifies Real line bundles in the sense of Atiyah. Thes...
The Radial-Hedgehog Solution in Landau--de Gennes' theory
Radial-Hedgehog Solution Landau--de Gennes' theory
2010/12/10
We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgeho...
On the structure of systematic perturbation theory with unstable fields
perturbation theory unstable fields
2010/11/2
Discussed is the structure of non-trivial counterterms that occur in the systematic gauge-invariant perturbation theory with unstable fields introduced in [hep-ph/9802307].
We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-ran...