Projects from Prof. Dr. Igor Burban
Algebra
SPP 1388: Representation Theory
Representation theory is a cross-disciplinary branch of mathematics with a wide range of applications in mathematics and in the sciences. Chemistry uses representation theory for instance to investigate symmetries of molecules, while quantum mechanics is a classical area of applications in physics. Further applications in physics and related areas ...
Duration: 01/2012 - 12/2016
Tame derived categories and their applications in algebraic geometry, representation theory, singularity theory and mathematical physcics
The technique of derived and triangulated categories is a universal language in which a synthesis of concepts and methods of various mathematical fields is accumulated. With its help one can apply concepts and results from algebraic geometry in compact formulation and solution of complicated analytic problems, a well-known example of which is the ...
Duration: 01/2007 - 12/2013
Triangulated categories and associative algebras in the geometry of singular varieties
The project belongs to algebraic geometry, homological algebra and representation theory in its interaction with theoretical physics. In the given research projects we can underline three guiding lines: - study of derived categories of coherent sheaves on singular varieties and their behavior in families, in particular in the case of degeneracies ...
Duration: 01/2005 - 12/2007