Displaying similar documents to “Spectral theory of translation surfaces : A short introduction”

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

Similarity:

We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...

Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper, Barak Weiss (2012)

Annales de l’institut Fourier

Similarity:

We study infinite translation surfaces which are ℤ -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Decompositions of an Abelian surface and quadratic forms

Shouhei Ma (2011)

Annales de l’institut Fourier

Similarity:

When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

On some flat connection associated with locally symmetric surface

Maria Robaszewska (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0....