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 …

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 …

We show that the Quot scheme $\text {Quot} _ {\mathbf {A}^ 3}(\mathcal {O}^ r, n) $ admits a
symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the …

Let $ S $ be a K3 surface. We study the reduced Donaldson-Thomas theory of the cap
$(S\times\mathbb {P}^ 1)/S_ {\infty} $ by a second cosection argument. We obtain four main …

In this article, we study quasimaps to moduli spaces of sheaves on a $ K3 $ surface S. We
construct a surjective cosection of the obstruction theory of moduli spaces of $\epsilon …

There are two natural ways to count stable pairs or Joyce-Song pairs on $ X=\mathrm
{K3}\times\mathbb C $; one via weighted Euler characteristic and the other by virtual …

We prove the crepant resolution conjecture for Donaldson–Thomas invariants of hard
Lefschetz 3-Calabi–Yau (CY3) orbifolds, formulated by Bryan–Cadman–Young, interpreting …

We prove the elliptic transformation law of Jacobi forms for the generating series of
Pandharipande–Thomas invariants of an elliptic Calabi–Yau threefold over a reduced class …

As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-
Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using …