Uwe Kähler
Assistant Professor with Agregação
Mathematics Department 
Universidade de Aveiro
Campus Universitário de Santiago
 3810-193 Aveiro, Portugal
Tel: +351 234372549


1. What are your personal perspectives as a researcher?
Like any mathematician I would like to found my own mathematical school, i.e. getting students and fellow researchers to understand and follow my approach to Mathematics. I also would like to find the right balance between „Pure“ and „Applied“ research. This means on one hand creating a method in terms of an abstract theory while on the other hand looking into the practical implementation. Usually, mathematical algorithms have the problem that they are either too theoretical (work only with academic examples) or that they have no theoretical justification (seems to work if one looks at examples, case studies). Getting both sides right, i.e. developing a method which is justified by a mathematical theory and works well in practical cases happens not that often. 

2. In your opinion, what are the biggest challenges in your area of research?
There are several. Probably the biggest challenge is the large gap between the increasingly sophisticated methods used by the specialists and the standard methods normal researchers know from their mathematical education. This leads to a lack of communication and dissemination of ideas as well as increasingly hard efforts of young researchers to catch up with the experts.
Apart from that there is the curse of dimensionality (anything being done in 3D and higher requires very high computational costs) and the focus on algebraisation in favor of geometric calculations. This leads to an unhealthy imbalance between the two approaches. 
From a pure scientific point of view the biggest challenge looks to me the construction of a function theory over higher non-commutative structures. Nowadays, it is well known how to do it for simple symmetries, like SU(2), but other cases remain difficult. This has connections with many problems, for instance, in extending Hörmander’s principal symbol calculus to a full symbol calculus.

3. Where are the strengths of the UA in your opinion?
In the first place we have many young researchers with high motivation. At least in the Department of Mathematics there are no pre-determined areas of Science which allows our researchers to look out for new areas and explore new opportunities. There is a large support from colleagues and administration which allows researchers to pursue top-level research within the constrains of a „small“ university with limited resources. It also has a beautiful campus and a nice ambience which makes it easier to invite top-level researchers for short research stays.

4. Could you give one idea to improve research in UA?
At the research day one should not only speak about results, but also about problems. Presenting a kind of „collection“ of problems which are currently considered hard problems or problems in „standby“ from each research center could lead to a bigger interaction between researchers from different areas. 

última atualização a 31-10-2014

About me

Uwe Kähler is a mathematician with various interests, ranging from abstract harmonic analysis in higher dimensions to problems in diffraction tomography. His main contributions are in the theory of discrete functions, where he successfully establish a higher dimensional discrete counterpart to Complex Analysis, and currently investigates its applications to boundary value problems, and in Harmonic Analysis over non-commutative Structures. In this last topic, emphasis goes to the construction of wavelets and Gabor frames over spin structures and their applications to diffraction tomography, and well as the study of monogenic signals for treatment of images.

Born in 1971, Uwe Kähler entered Chemnitz University of Technology in 1986 and received his PhD in 1998. After 1998 he was a Pos-Doc of FCT in Aveiro, working within the group Complex and Hypercomplex Analysis, and is currently Assistant Professor with Habilitation at the University of Aveiro and researcher in CIDMA - UA. He teaches at undergraduate, Master, and PhD level, and has been invited as lecturer in leading research institutes such as Imperial College London, Ludwig-Maximilian University Munich, TU Munich, Konrad-Zuse Institute Berlin, and Rolf-Nevanlinna-Institute Helsinki. He published more than 80 scientific papers.

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