GADEPs Focused Meeting - Differential Equations and Prime Numbers - An Effective Proof of the p-Curvature Conjecture for Order One Equations

Explore an advanced mathematical lecture presenting an effective proof of the p-curvature conjecture for order one equations. Delve into the intersection of differential equations and prime number theory as Lucas Pannier from Université de Versailles Saint-Quentin demonstrates rigorous mathematical techniques and proofs in this specialized area of pure mathematics. Learn about the p-curvature conjecture, a significant problem in algebraic geometry and number theory that relates to the behavior of differential equations in positive characteristic. Examine the mathematical framework underlying order one differential equations and understand how they connect to prime number properties. Discover the proof techniques and analytical methods used to establish effective bounds and results for this important conjecture. Gain insights into current research directions in the field where differential equations meet number theory, and understand the implications of this work for broader mathematical theory. This presentation is part of the GADEPs (Geometric Aspects of Differential Equations and Prime Numbers) focused meeting series, targeting researchers and advanced students in mathematics with strong backgrounds in algebraic geometry, differential equations, and number theory.