In this thesis, we study questions from enumerative geometry of local surfaces. We give a definition for local Gromov–Witten and local Gopakumar–Vafa invariants for some singular surfaces as a ...

We review the string/gauge theory duality relating Chern-Simons theory and topological strings on noncompact Calabi-Yau manifolds, as well as its mathematical implications for knot invariants and ...

We introduce a Transformer-based approach to computational enumerative geometry, specifically targeting the computation of $\psi$-class intersection numbers on the moduli space of curves. Traditional ...

Abstract: In enumerative algebraic geometry, we try to compute invariants of varieties, usually defined as certain counts of objects in an associated moduli space. In this talk, we give an ...

Quantum K‐theory represents a significant advancement in our understanding of both algebraic geometry and representation theory by integrating quantum corrections into classical K‐theory. This ...

I will introduce a new framework for studying the enumerative geometry of general algebraic stacks, which is intrinsic to the stack, and generalizes existing enumerative theories for moduli stacks of ...

Abstract: Cramer's theorem from 1750 is a beautiful illustration of enumerative geometry: there is exactly one curve in the plane if we impose the right number and type of constraints. More recently, ...

Moduli spaces of curves and abelian varieties, tautological classes, Siegel and Teichmüller modular forms, and their relation to the cohomology of moduli spaces, linear orbits of plane curves ...