Prof Warwick Tucker

Research Overview

My research aims at advancing the frontiers of computer-aided proofs in mathematical analysis. This area of research is geared to deal with problems that cannot be solved by traditional mathematical methods alone. Typically, such problems have a global component as well as a non-linear ingredient. Hard problems of this type have traditionally been studied through numerical computations alone, and therefore our knowledge of these lack the rigour demanded by a mathematical proof. My research aims to bridge the gap between a numerically observed phenomenon, and its mathematical counterpart.

Selected Publications

[1] Galias, Zbigniew ; Tucker, Warwick. "Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor". In: Journal of Differential Equations. 2019 ; Vol. 266, No. 5. pp. 2408-2434.

[2] Mitrea, Irina ; Ott, Katharine ; Tucker, Warwick. "Invertibility Properties of Singular Integral Operators Associated with the Lamé and Stokes Systems on Infinite Sectors in Two Dimensions". In: Integral Equations and Operator Theory. 2017 ; Vol. 89, No. 2. pp. 151-207.

[3] Figueras, Jordi Lluís ; Tucker, Warwick ; Villadelprat, Jordi. "Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals". In: Journal of Differential Equations. 2013 ; Vol. 254, No. 8. pp. 3647-3663.

[4] Johnson, Tomas ; Tucker, Warwick. "Rigorous parameter reconstruction for differential equations with noisy data". In: Automatica. 2008 ; Vol. 44, No. 9. pp. 2422-2426.

[5] Tucker, Warwick. "A Rigorous ODE Solver and Smale's 14th Problem". In: Foundations of Computational Mathematics. 2002 ; Vol. 2, No. 1. pp. 53-117.