Three questions in Gromov-Witten theory

Abstract

This article accompanies my ICM talk in August 2002. Three conjectural directions in Gromov-Witten theory are discussed: Gorenstein properties, BPS states, and Virasoro constraints. Each points to basic structures in the subject which are not yet understood.

10 pages

References in corpus (8)

• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• Quantum Cohomology and Virasoro Algebra
• Virasoro constraints and the Chern classes of the Hodge bundle
• Hodge integrals and degenerate contributions
• BPS states of curves in Calabi--Yau 3--folds
• Gromov-Witten theory, Hurwitz theory, and completed cycles
• M-Theory, Topological Strings and Spinning Black Holes
• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)

Cited by in corpus (43)

• Curve counting via stable pairs in the derived category
• Tautological relations and the r-spin Witten conjecture
• Enumerative geometry of Calabi-Yau 4-folds
• Riemann-Hilbert problems from Donaldson-Thomas theory
• 13/2 ways of counting curves
• The structure of the tautological ring in genus one
• The Gorenstein conjecture fails for the tautological ring of ${\bar{\mathcal{M}}}_{2,n}$
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Tautological and non-tautological cohomology of the moduli space of curves
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras
• Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds
• The kappa ring of the moduli of curves of compact type: II
• Calculating intersection numbers on moduli spaces of pointed curves
• The tautological rings of the moduli spaces of stable maps
• Riemann-Hilbert problems for the resolved conifold
• A Comparison Theorem for Gromov-Witten Invariants in the Symplectic Category
• A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
• The local Gromov-Witten theory of curves
• Algebraic structures on the topology of moduli spaces of curves and maps
• Invariance of tautological equations I: conjectures and applications
• The tautological ring of ${\mathcal{M}}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relations
• Notes on the proof of the KKV conjecture
• The kappa classes on the moduli spaces of curves
• Log BPS numbers of log Calabi-Yau surfaces
• A compactification of the space of maps from curves
• Virasoro constraints for stable pairs on toric 3-folds
• New calculations in Gromov-Witten theory
• Orthogonal Quantum Group Invariants of Links
• Cycles on curves and Jacobians: a tale of two tautological rings
• Tautological classes with twisted coefficients
• Poincaré duality of wonderful compactifications and tautological rings
• $PG{L}_2$-equivariant strata of point configurations in ${\mathbb{P}}^1$
• Algebraic cobordism revisited
• Compactified Picard stacks over the moduli stack of stable curves with marked points
• Towards the geometry of double Hurwitz numbers
• Lower Bounds for Enumerative Counts of Positive-Genus Real Curves
• A characterization of Gorenstein Hilbert functions in codimension four with small initial degree
• Relative maps and tautological classes
• Open problems (for AGNES)
• Genus zero Gopakumar-Vafa invariants of contractible curves
• Topological Recursion Relations on ${\bar{\mathcal{M}}}_{3,2}$
• On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley