Hilbert schemes of points and infinite dimensional Lie algebras

Content: Hilbert schemes of points on surfaces: Basic results on Hilbert schemes of pointsThe nef cone and flip structure of $(\mathbb{P}^2)^{[n]}$Hilbert schemes and infinite dimensional Lie algebras: Hilbert schemes and infinite dimensional Lie algebrasChern character operatorsMultiple $q$-zeta values and Hilbert schemesLie algebras and incidence Hilbert schemesCohomology rings of Hilbert schemes of points: The cohomology rings of Hilbert schemes of points on surfacesIdeals of the cohomology rings of Hilbert schemesIntegral cohomology of Hilbert schemesThe ring structure of $H^*_{\textrm{orb}}(X^{(n)})$Equivariant cohomology of the Hilbert schemes of points: Equivariant cohomology of Hilbert schemesHilbert/Gromov-Witten correspondenceGromov-Witten theory of the Hilbert schemes of points: Cosection localization for the Hilbert schemes of pointsEquivariant quantum operator of Okounkov-PandharipandeThe genus-0 extremal Gromov-Witten invariantsRuan's Cohomological Crepant Resolution ConjectureBibliographyIndex