Austrian researcher Christian Lubich led a plenary audience at ICM 2018 through “Dynamics, numerical analysis and some geometry”.  The Innsbruck-based mathematician described the varied nature of geometric aspects that influence dynamics.  He based his discussion in symplectic integrators for Hamiltonian ordinary and partial differential equations, and applied his research to algorithm design and network approximations in quantum mechanics.

 

“A good algorithm should respect the structure of the problem,” he said. Algorithm design is an area of growing interest for many mathematicians with increased industrial demand for automation. Applied to timescales, numerical analysis has far reaching implications for studying dynamic systems in oscillation. Lubich’s previous work focused on resolving conflicts in approximation of equations by low-rank representation. His reasearch areas connect through work with numerical simulations.

 

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Lubich has been a professor of Numerical Mathematics at the  University of Tübingen in Germany since 1994. In 1985, he  was awarded the Research Prize of the City of Innsbruck. He also received the Dahlquist Prize of the SIAM in 2001.