Gromov-Witten theory

Gromov-Witten theory studies the way curves (think of smooth, continuous shapes like loops or surfaces) can fit into more complex spaces, such as geometric shapes known as manifolds. It combines techniques from algebraic geometry and topology to count how many of these curves can exist within a given space, factoring in constraints like intersections. This theory has profound implications in various fields of mathematics and theoretical physics, as it helps link different concepts, such as counting particles in string theory or understanding shape transformations in geometry.