**Some 'What', 'Why' and 'How' on Row Reducing Matrices over Ore Polynomial Rings**

**Prof. Johan S. H. Rosenkilde**

Technical University of Denmark

DTU COMPUTE

Department of Applied Mathematics and Computer Science

Ore polynomials, also known as skew polynomials, are non-commutative polynomials which can algebraically model differential equations, time-dependent systems, linear maps over finite fields, and more. Matrices over Ore polynomial rings can model systems of these objects and have found applications in diverse areas. Computing reduced normal forms of such matrices can be useful for checking system equivalence or finding special elements in the space, e.g. shortest vectors; the latter can be applied to decoding certain rank and subspace metric codes. In this talk I will introduce Ore polynomial rings, some important examples hereof, and describe some recent work on computing certain reduced normal forms of matrices of Ore polynomials, with an emphasis on controlling coefficient growth.

Johan Rosenkilde received his Master's degree in computer science in 2010 and a Ph.D. in mathematics in 2013, both at the Technical University of Denmark. He was subsequently a post-doc first at Ulm University, Germany and then at Inria Saclay, France. Since 2015 he has been assistant professor at the Technical University of Denmark. His research interests include algebraic coding theory and computer algebra.