Counting Lattice Points in Ellipsoids and the Central Limit Theorem for Quadratic Forms

Watch a 48-minute mathematics lecture exploring classical lattice point counting problems for ellipsoids and their connections to probability theory. Delve into explicit error bounds for dimensions five and higher, examining both historical and contemporary findings. Learn about the relationship between these error estimates and the multivariate central limit theorem in Probability, while understanding the significance of gap principles in bounding Fourier integrals. Presented at the Hausdorff Center for Mathematics, this advanced mathematical discussion bridges number theory and probability through the examination of quadratic forms and their properties.