Melnikov Functions Appearing in Polynomial Hamiltonian Perturbations
59:58Definable Norms on Riemann-Zariski Spaces
1:01:26On the Completions of General Period Mappings
1:04:02Hodge-Theoretic Anabelian Geometry
58:54(Quasi)-Periods Functions and Derivatives of Period Maps
1:00:19Some Effective Special Point Results
55:15Matrix Points on Varieties
1:01:20The Dynamical Schinzel-Zassenhaus Conjecture and the Transfinite Diameter of Trees
1:03:50A Syntomic Perspective on Integral Canonical Models
1:00:14Heights of Gross-Schoen and Ceresa Cycles
54:41Definable Quotient Spaces for Unlikely Intersection Problems
59:55Constructing Holomorphic Functions on Universal Coverings of Complex Algebraic Varieties
1:09:35Galois Action on Higher etale Homotopy Groups
1:06:55Matroids and the Integral Hodge Conjecture for Abelian Varieties
1:06:12Ax-Schanuel and the Rank One Riemann-Hilbert Correspondence
59:04Melnikov Functions Appearing in Polynomial Hamiltonian Perturbations
This lecture explores Melnikov functions as higher-order approximations in Hilbert's 16th problem, particularly for polynomial Hamiltonian perturbations, building on the vanishing of first-order Abelian integrals.
Workshop on Recent Developments in Hodge Theory and O-minimality