Markus Püschel's research is at the intersection of engineering, computer science, and mathematics. Below are two examples.
Fast changing and increasingly parallel computer architectures pose a difficult task for developers of high performance software in signal processing, communication, and scientific computing. The goal of SPIRAL is to completely automate the implementation and optimization of performance-critical functionality. SPIRAL builds on and combines techniques from compilers, programming languages, symbolic computation, mathematics, machine learning, and computer architecture.
The goal of SMART is to explore and exploit the relationship between signal processing and abstract algebra. The most comprehensive example is a new, axiomatic approach and generalization of signal processing, called "Algebraic Signal Processing Theory," that we developed. Benefits of this theory include a comprehensive theory of fast algorithms and the derivation of new SP frameworks.