Polynomial System Solving
Currently my research projects discuss problems in (but are not restricted to) Computer algebra, Symbolic computation, Polynomial system solving and all its various applications in Algebraic geometry, Cryptography, Robotics and many many more.
Modern computers paired with sophisticated mathematical software tools allow for success stories in mathematics and its application areas which were previously unimaginable. Taking center stage in science, engineering, and industry, effective computational methods have become an integral part of our daily lives. Somewhat masked by the ubiquity of tools based on fast linear algebra, recent progress in theory and praxis has led to the proliferation of nonlinear methods, notably for systems of multivariate polynomial equations. So it is fair to say that these methods are now at the forefront of exciting developments.
Following my firm belief that the tasks of designing innovative mathematical software and of solving complex research problems using computational methods are strongly mutually dependent, my ambitious goal is to considerably push the computational boundaries of nonlinear algebra, notably addressing polynomial system solving. Thus, applying the resulting algorithms and corresponding software tools, we can solve challenging problems which have been intractable so far in mathematics and applied sciences.