Regular and positive noncommutative rational functions

Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this talk regular noncommutative rational functions $r$ will be characterized via the properties of their (minimal size) linear systems realizations $r=c^* L^{-1}b$. Our main result states that $r$ is regular if and only if $L=A_0+\sum_jA_j x_j$ is privileged. Roughly speaking, a linear pencil $L$ is privileged if, after a finite sequence of basis changes and restrictions, the real part of $A_0$ is positive definite and the other $A_j$ are skew-adjoint. Afterwards I will speak about a solution to a noncommutative version of Hilbert\u27s 17th problem: a positive regular noncommutative rational function is a sum of squares. The talk is based on the joint work with I. Klep and J. E. Pascoe

Convergence in shape of Steiner symmetrizations

There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examples show that Steiner symmetrization along a sequence of directions whose differences are square summable does not generally converge. (Note that this may happen even with sequences of directions which are dense in S^{n-1}.) Here we show that such sequences converge in shape. The limit need not be an ellipsoid or even a convex set. We also deal with uniformly distributed sequences of directions, and with a recent result of Klain on Steiner symmetrization along sequences chosen from a finite set of directions.Comment: 11 page

The Ethnographer Unbared: Reflections on Ethnographic Media Research Processes

In diesem Artikel gehe ich auf einige der Herausforderungen ein, mit denen ich bei meiner ethnografischen Arbeit über Medienproduktion und -konsum am Balkan konfrontiert war – insbesondere in der Zeit zwischen den 1990er und 2000er Jahren im ehemaligen Jugoslawien. Ich reflektiere, wie sich mein persönlicher und intellektueller Hintergrund mit meiner Feldforschung in einem Kontext überschnitt, in dem eine ständige (Neu-)Verhandlung meiner eigenen Identität erforderlich war, nicht nur in Bezug auf meine Teilnehmer*innen und Forscherkolleg*innen in der Region, sondern auch auf die vorherrschenden akademischen institutionellen Praktiken. Der Artikel ist kein auto-ethnografischer Bericht, sondern eher eine Reflexion über Feldforschung an Orten, die von großen wirtschaftlichen, politischen und sozialen Unruhen geprägt sind. Als junge Wissenschaftlerin, die im Bereich der Kultur- und Medienwissenschaften arbeitet, sah ich mich schon früh mit dem Problem konfrontiert, von einigen Forschungsteilnehmer*innen und Kolleg*innen nicht ernst genommen zu werden. Ich musste meinen Weg durch die verschiedenen kulturellen Praktiken finden und verhandeln, um eine erfolgreiche standortübergreifende Forschung durchführen zu können.In this article, I unpack some of the challenges I faced doing ethnographic work on media production and consumption in the Balkans—particularly in the period of the 1990s-2000s in former Yugoslavia. I reflect on how my personal and intellectual background intersected with my fieldwork in a context that demanded constant (re)negotiation of my own identity, in relation not only to my participants and research colleagues in the region, but also to prevailing academic institutional practices. The article is not an autoethnographic account per se, but more a reflection on the research process in fieldwork sites experiencing great economic, political and social turmoil. As a young female researcher working in the area of cultural and media studies, I faced the problem of not being taken seriously by some research participants and colleagues early on, and had to identify and negotiate my way into the various cultural practices that would enable me to conduct effective multi-site research

Free loci of matrix pencils and domains of noncommutative rational functions

Consider a monic linear pencil $L(x)=I-A_1x_1-\cdots-A_gx_g$ whose coefficients $A_j$ are $d\times d$ matrices. It is naturally evaluated at $g$-tuples of matrices $X$ using the Kronecker tensor product, which gives rise to its free locus $Z(L)=\{X:\det L(X)=0\}$. Our main result is the following: $Z(L)\subseteq Z(L\u27)$ if and only if the natural map sending the coefficients of $L\u27$ to the coefficients of $L$ induces a homomorphism $A\u27/\operatorname{rad}A\u27\to A/\operatorname{rad}A$. Since linear pencils are a key ingredient in studying noncommutative rational functions via linear systems realization theory, the above result leads to a characterization of all noncommutative rational functions with a given domain. Finally, an answer to a quantum version of Kippenhahn\u27s conjecture on linear pencils will be given: if hermitian matrices $A_1,\dots,A_g$ generate M_d(\C) as an algebra, then there exist hermitian matrices $X_1,\dots,X_g$ such that $\sum_iA_i\otimes X_i$ has a simple eigenvalue. The talk is based on the joint work with I. Klep

Nostalgia for Greater Serbia: Media coverage of Radovan Karadžic’s arrest

The arrest of former Bosnian Serb leader Radovan Karadžic in July 2008 triggered wide-spread international interest and provided the opportunity for the Serbian public and its media to reflect upon the role of Serbia in the Yugoslav wars of the 1990s. Karadžic was a Bosnian-Serb president of the self-proclaimed Serbian republic within Bosnia and Herzegovina, and was indicted for genocide and crimes against humanity in 1995. On the basis of critical discourse analysis, we argue that Television Serbia, while covering Karadžic's arrest, constructed a nationalistic discourse by invoking nostalgia for Greater Serbia in ways that suppressed or concealed any connection between Karadžic specifically, the Serbs in general, and especially the current government with war crimes in Bosnia and Herzegovina. At the same time this discourse celebrated Serbia as a superior nation as it progressed toward inclusion in the European Union