Research

The moduli space of curves is a cornerstone object in mathematics and theoretical physics, underpinning theories from Gromov–Witten invariants to string theory.  We identify a striking hidde n  regularity: The distribution of its Betti numbers converges to the Gaussian function. This result demonstrates that complicated geometric structures can exhibit the same statistical predictability found in nature. Furthermore, we identify other fundamental moduli spaces, such as the Hilbert scheme, that do not exhibit asymptotic normality. This proposes a probabilistic approach for classifying geometric spaces based on their asymptotic behavior.