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• #### Geometry of Free Loci and Factorization of Noncommutative Polynomials ﻿

[OWP-2017-23] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)
The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...
• #### A real algebra perspective on multivariate tight wavelet frames ﻿

[OWP-2012-11] (Mathematisches Forschungsinstitut Oberwolfach, 2012-08-13)
Recent results from real algebraic geometry and the theory of polynomial optimization are related in a new framework to the existence question of multivariate tight wavelet frames whose generators have at least one vanishing ...