A bstract We use the GKZ description of periods and certain classes of relative periods on
families of Barth-Nieto Calabi-Yau (l− 1)-folds in order to solve the l-loop banana amplitudes …

A bstract We give evidence that the all genus amplitudes of topological string theory on
compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic …

We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a
polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs. For …

Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov–Witten
theory of the Calabi–Yau threefold S * ES× E for all curve classes which are primitive in the …

Let $ A=(a_1,\ldots, a_n) $ be a vector of integers with $ d=\sum_ {i= 1}^ n a_i $. By partial
resolution of the classical Abel-Jacobi map, we construct a universal twisted double …

Block and Göttsche have defined aq-number refinement of counts of tropical curves in R^ 2
R 2. Under the change of variables q= e^ iu q= e iu, we show that the result is a generating …

We consider the boundary dual of AdS3xS3xK3 for NS5-flux Q5= 1, which is described by a
sigma model with target space given by the d-fold symmetric product of K3. Building on …

THE KATZ–KLEMM–VAFA CONJECTURE FOR K3 SURFACES Page 1 Forum of Mathematics,
Pi (2016), Vol. 4, e4, 111 pages doi:10.1017/fmp.2016.2 1 THE KATZ–KLEMM–VAFA …

We introduce marked relative Pandharipande-Thomas (PT) invariants for a pair (X, D) of a
smooth projective threefold and a smooth divisor. These invariants are defined by …

We conjecture that the generating series of Gromov–Witten invariants of the Hilbert schemes
of n points on a K3 surface are quasi-Jacobi forms and satisfy a holomorphic anomaly …