Curve-Counting with Fixed Domain in Complex Varieties

Explore a mathematical lecture delving into the fixed-domain curve-counting problem and its two distinct approaches in complex geometry. Learn about counting pointed curves with fixed complex structure in target variety X, examining both the virtual count method using Gromov-Witten theory and the geometric count approach. Understand how these counting methods, while conjectured to align under sufficient positivity conditions, can produce different results. Discover recent developments and ongoing research questions in this field, including collaborative work with Alessio Cela, Gavril Farkas, and Rahul Pandharipande from the perspective of Humboldt-Universität zu Berlin researcher Carl Lian.