Speaker: Marc Mezzarobba
Abstract: Linear differential equations with polynomial coefficients in a complex
variable appear naturally in fields such as combinatorics, algebraic geometry, and mathematical physics. Their numerical solution, and in particular that of so-called connection problems between regular singular points, finds applications that include the high-precision computation of values of Feynmann integrals, volumes of semi-algebraic sets, or more generally periods of algebraic varieties, the asymptotic expansion of linearly recurrent sequences, and the factorization of linear differential operators. In this talk, I will give a demonstration of a numerical ODE solver that focuses on this very special class of equations, supports arbitrary-precision computations, and provides rigorous error bounds along with the numerical results. I will also demonstrate software for some of the applications listed above built on top of this solver.
variable appear naturally in fields such as combinatorics, algebraic geometry, and mathematical physics. Their numerical solution, and in particular that of so-called connection problems between regular singular points, finds applications that include the high-precision computation of values of Feynmann integrals, volumes of semi-algebraic sets, or more generally periods of algebraic varieties, the asymptotic expansion of linearly recurrent sequences, and the factorization of linear differential operators. In this talk, I will give a demonstration of a numerical ODE solver that focuses on this very special class of equations, supports arbitrary-precision computations, and provides rigorous error bounds along with the numerical results. I will also demonstrate software for some of the applications listed above built on top of this solver.