We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal A3-singularity of the weighted projective space ℙ(1,3,4,4) using the theory of deformations of surfaces with An-singularities. We use this result to check Ruan’s conjecture for the stack ℙ(1,3,4,4).

In the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n and multiplier eiθ are known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.

We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.

We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number #V(G) of the vertices. We give Cohen-Macaulay criteria for such graphs.

In this note, we introduce an approximation of harmonic maps via a sequence of exponentially harmonic maps. We then reestablish the existence theorem of harmonic maps due to Eells and Sampson.