Matthias Kawski

Biography

Matthias Kawski develops, and employs, tools from differential geometry and algebraic combinatorics to study nonlinear control systems. Controlled dynamical systems are distinguished from classical ones by their input and output channels that allow one to interact with the systems. Prototypical is the difference between planetary motion and motion of a human-made satellite. Classically one asks: Where will the system go? When is the next eclipse? Is the solar system stable? Control theory asks inverse questions: Can I get there, and if so how? How optimally? Is the system stabilizable? Applications are ubiquitous, from mechanical and electrical systems, to finance, biomedicine and beyond. Kawski employs diverse mathematical tools, from Lie algebras to combinatorial Hopf algebras, to uncover geometric properties of control systems on manifolds, and to design efficient algorithms suiting the inherently nonassociative nature of noncommuting flows (control actions).

Research Interest

Nonlinear control theory -- using tools from differential geometry to combinatorial Hopf algebras. Using technology, especially interactive dynamic visualization, in mathematics education.