ar X iv : 0 70 5 . 37 56 v 1 [ m at h . N T ] 2 5 M ay 2 00 7 On the Lenstra constant associated to the Rosen continued fractions

ar X iv : 0 80 5 . 37 89 v 1 [ m at h . A P ] 2 4 M ay 2 00 8 The balance between diffusion and absorption in semilinear parabolic equations ∗

Let h : [0,∞) 7→ [0,∞) be continuous and nondecreasing, h(t) > 0 if t > 0, and m,q be positive real numbers. We investigate the behavior when k → ∞ of the fundamental solutions u = uk of ∂tu − ∆u m + h(t)u = 0 in Ω × (0, T ) satisfying uk(x, 0) = kδ0. The main question is wether the limit is still a solution of the above equation with an isolated singularity at (0, 0), or a solution of the asso...

ar X iv : 0 70 5 . 31 41 v 1 [ as tr o - ph ] 2 2 M ay 2 00 7 The SARG Planet Search

ar X iv : 0 70 5 . 12 53 v 1 [ m at h . A C ] 9 M ay 2 00 7 DUALITIES AND INTERSECTION MULTIPLICITIES

Let R be a commutative, noetherian, local ring. Topological Q– vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

ar X iv : 0 70 5 . 38 12 v 1 [ m at h . D S ] 2 5 M ay 2 00 7 DYNAMICS OF THE TEICHMÜLLER FLOW ON COMPACT INVARIANT SETS

Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is...

ar X iv : 0 70 5 . 39 48 v 1 [ m at h . R T ] 2 7 M ay 2 00 7 DEGENERATION OF A - INFINITY MODULES

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasiisomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Z...