I would be willing to bet that whatever formulations of quantum field theory we have now are preliminary ... - Robbert Dijkgraaf

Mirror symmetry is concerned with counting the number of holomorphic curves on Calabi-Yau manifolds, i.e. compact Kähler manifolds X with trivial canonical bundle K_X.

The last two years have seen the emergence of a beautiful new subject in mathematical physics. It manages to combine a most exotic range of disciplines: two-dimensional quantum field theory, intersection theory on the moduli space of Riemann surfaces, integrable hierarchies, matrix integrals, random surfaces, and many more. The common denominator of all these fields is two-dimensional quantum gravity or, more general, low-dimensional string theory.