We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian
knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya …

In this paper, we propose an ansatz for defining Gopakumar–Vafa invariants of Calabi–Yau
threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a …

We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …

We conjecture an expression for the dimensions of the Khovanov–Rozansky HOMFLY
homology groups of the link of a plane curve singularity in terms of the weight polynomials of …

We prove that the intersection cohomology (together with the perverse and the Hodge
filtrations) for the moduli space of one-dimensional semistable sheaves supported in an …

In recent years, intersection homology and perverse sheaves have become indispensable
tools for studying the topology of singular spaces. This book provides a gentle introduction to …

We relate the mixed Hodge structure on the cohomology of open positroid varieties (in
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …

In the past 20 years, compactifications of the families of curves in algebraic varieties X have
been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable …

We define refined invariants which “count” nodal curves in sufficiently ample linear systems
on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit …