We develop a theory of Bridgeland stability conditions and moduli spaces of semistable
objects for a family of varieties. Our approach is based on and generalizes previous work by …

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 …

Fix a Calabi-Yau 3-fold $ X $ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\i-
Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting …

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We derive conjectures, called genus 1 Enumerative mirror symmetry for moduli spaces of
Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm …

We study slope-stable vector bundles and Bridgeland stability conditions on varieties which
are a quotient of a smooth projective variety by a finite abelian group $ G $ acting freely. We …

We prove the period-index conjecture for unramified Brauer classes on abelian threefolds.
To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional …

We construct a subset of the space of stability conditions for any projective threefold with an
ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result …

We determine a full component of the space of stability conditions on $ D^ b (E^ 3) $ where
$ E $ is an elliptic curve without complex multiplication. The component has complex …

We study slope-stable vector bundles and Bridgeland stability conditions on varieties which
are a quotient of a smooth projective variety by a finite group G acting freely. We show that …