About
I am a mathematician specialising in Algebra (in particular studies of various algebraic structures such as rings, modules, corings, comodules, Hopf algebras etc.), Noncommutative Geometry (both algebraic and differential, with particular stress put on symmetry aspects), Category Theory and some aspects of Mathematical Physics (quantum groups, integrable systems). I am the author or co-author of a monograph and over 110 papers (written with ca 45 co-authors). The revival and significant development of the theory of corings (new AMS classification category has been created for corings and comodules as a result of this activity) is perhaps the most notable achievement of my research programme.
This work was started by M Takeuchi's observation that entwined modules can be seen as comodules of a coring (read: co-ring). This observation was first exploited in [T. Brzeziński, The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties, Algebras and Representation Theory 5: 389-410, 2002] and immediately attracted attention of wider mathematical community (according to MathSciNet, this paper is the second most cited article out of over 1000 papers published in journal Algebras and Representation Theory). Initial studies of the structure of corings resulted in a very well received monograph [T. Brzeziński & R. Wisbauer, Corings and Comodules, Cambridge University Press, Cambridge 2003] and further studies quickly followed. The attractiveness of corings lies in the fact that they combine various areas of mathematics: Hopf algebra theory, noncommutative geometry (both differential and algebraic - which are quite separate theories), ring and module theory and category theory (including, in particular, its applications to computer science). An inclusion of corings as a topic in the American Mathematical Society Mathematics Subject Classification from 2010 can serve as an indicator of the recognition of corings by the international mathematical community.