We enumerate all Shimura curves XD 0 (N) of genus at most two: there are exactly 858 such curves, up to equivalence. The elliptic modular curve X0(N) is the quotient of the completed upper halfplane H∗ by the congruence subgroup Γ0(N) of matrices in SL2(Z) that are upper triangular modulo N ∈ Z>0. The curve X0(N) forms a coarse moduli space for (generalized) elliptic curves equipped with a cycl...

The amoeba of a Laurent polynomial f ∈ C[z 1 , . . . , z n ] is the image of its zero set V(f) under the log-absolute-value map. Understanding the space of amoebas (i.e., the decomposition of the space of all polynomials, say, with given support or Newton polytope, with regard to the existing complement components) is a widely open problem. In this paper we investigate the class of polynomials ...

The at-most-once problem in shared memory asks for the completion of a number of tasks by a set of independent processors while adhering to “at most once” semantics. At-most-once algorithms are evaluated in terms of effectiveness, which is a measure that expresses the total number of tasks completed at-most-once in the worst case. Motivated by the lack of deterministic solutions with high effec...

A tree is called a caterpillar if all its leaves are adjacent to the same its path, and the path is called a spine of the caterpillar. Broersma and Tuinstra proved that if a connected graph G satisfies σ2(G) ≥ |G| − k + 1 for an integer k ≥ 2, then G has a spanning tree having at most k leaves. In this paper we improve this result as follows. If a connected graph G satisfies σ2(G) ≥ |G|−k+1 and...

We announce the construction up to isomorphism of the 49 910 529 484 groups of order at most 2000.