Janko Böhm: ​​​​​​​Massively parallel computations in computer algebra

Abstract: The design of parallel algorithms is a fundamental task in computer algebra. Massively parallel computations relying on transparent environments for separating computation and coordination have been a success story for many years in high performance numerical simulation. Combining the computer algebra system Singular for polynomial computations and the work-flow management system GPI-Space, which relies on Petri nets as its mathematical modeling language, we have developed a framework for massively parallel computations in commutative algebra and algebraic geometry.
In this talk I will discuss the structure, potential and performance of this framework, applying it to multiple test cases. These include a new algorithm for deciding smoothness of algebraic varieties based on the termination criterion of Hironaka's resolution of singularities, an algorithm for computing GIT-fans in geometric invariant theory, and the computation of tropical varieties with symmetry.

This talk is based on joint work with Dominik Bendle, Wolfram Decker, Anne Frühbis-Krüger, Franz-Josef Pfreundt, Mirko Rahn, Christian Reinbold, Yue Ren and Lukas Ristau.