In this paper, we present foundational material towards the development of a rigorous enumerative theory of stable maps with Lagrangian boundary conditions, i.e. stable maps from bordered Riemann ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

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 ...

Gromov-Witten invariants, which ''count'' curves (with appropriate extra conditions) on smooth projective varieties, were introduced more than two decades ago; motivated by high energy physics, they ...

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 ...

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 ...

Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted. A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying ...

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 ...

Abstact: The famous Kontsevich Recursion formula for curve counts in the plane may be proved via the WDVV equation for the Gromov Witten potential, closely related to the associativity of the Quantum ...

A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying glass. An illustration of a magnifying glass.