We prove a formula computing the Gromov-Witten invariants of genus zero with three marked points of the resolution of the transversal $A_3$-singularity of the weighted projective space $\mathbb{P}(1,3,4,4)$ using the theory of deformations of surfaces with $A_n$-singularities. We use this result to check Ruan’s conjecture for the stack $\mathbb{P}(1,3,4,4)$.

In the space of degree $d$ polynomials, the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier $e^{i\theta }$ 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 $I\left(G\right)$ is half of the number $♯V\left(G\right)$ 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.