Joana Pech-Alberich will give a talk on 02/24/2026.

In this talk we will review a proof for the Antunes-Freitas conjecture (2006): for regular $N$-sided polygons of fixed area, the first Dirichlet eigenvalue $\lambda_1(N)$ and the quotients $\lambda_1(N)/\lambda_1(N+1)$ are monotonically decreasing in $N$. The proof combines two approaches: sharp asymptotic expansions with rigorous error bounds (for $N \geq 64$) and computer-assisted proofs using interval arithmetic (for $N < 64$). This is joint work with Joel Dahne and Javier Gómez-Serrano.