Enumerative invariants in Algebraic Geometry'count'$\tau $-(semi) stable objects $ E $ with
fixed topological invariants $[E]= a $ in some geometric problem, using a virtual class $[{\cal …

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain
polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a …

By studying the properties of q-series Z^-invariants, we develop a dictionary between 3-
manifolds and vertex algebras. In particular, we generalize previously known entries in this …

Abstract In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective
surfaces is lifted to oriented C^* C∗-equivariant cohomology theories. Here we study the K …

What follows is a broad-brush overview of the recent synergistic interactions between
mathematics and theoretical physics of quantum field theory and string theory. The …

In this paper we consider three types of localization theorems for algebraic stacks:(i)
Concentration, or cohomological localization. Given an algebraic group acting on a scheme …

Supersymmetric D-branes supported on the complex two-dimensional base S of the local
Calabi–Yau threefold KS are described by semi-stable coherent sheaves on S. Under …

We compute tautological integrals over Quot schemes on curves and surfaces. After
obtaining several explicit formulas over Quot schemes of dimension-0 quotients on curves …

We study BPS spectra of D-branes on local Calabi-Yau threefolds O (-p) ⊕ O (p-2) → P^ 1 O
(-p)⊕ O (p-2)→ P 1 with p= 0, 1 p= 0, 1, corresponding to C^ 3/Z _ 2 C 3/Z 2 and the …

We conjecture a formula for the generating function of virtual χ _y χ y-genera of moduli
spaces of rank 2 sheaves on arbitrary surfaces with holomorphic 2-form. Specializing the …