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 …

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 present a brief overview of Moonshine with an emphasis on connections to physics.
Moonshine collectively refers to a set of phenomena connecting group theory, analytic …

We prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko–
Zagier differential equation for Jacobi forms. The transformation properties of the solutions …

Given an action of a finite group $ G $ on the derived category of a smooth projective variety
$ X $ we relate the fixed loci of the induced $ G $-action on moduli spaces of stable objects …

A banana manifold is a compact Calabi-Yau threefold, fibered by Abelian surfaces, whose
singular fibers have a singular locus given by a" banana configuration of curves". A basic …

We provide a definition of Vafa-Witten invariants for projective surface Deligne-Mumford
stacks, generalizing the construction of Tanaka-Thomas on the Vafa-Witten invariants for …

Let X be a complex K3 surface with an effective action of a group G which preserves the
holomorphic symplectic form. Let Z_ X, G (q)= n= 0^ ∞ e\left (Hilb^ n (X)^ G\right)\, q^ n-1 be …

A bstract Motivated by recent advances in Donaldson-Thomas theory, four-
dimensional\(\mathcal {N}\)= 4 string-string duality is examined in a reduced rank theory on …

K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of
their enumerative invariants have important consequences in black hole physics and in …