Research plan and experience

My field of interest is mathematical physics, more precisely the differential geometric, algebro-topologic, analytic background of classical and quantum field theories such as Yang-Mills and general relativity theory. This vivid branch of interdisciplinary science is in the intersection of current pure mathematics and theoretical physics. On the one hand the problems, questions often appear first in classical or quantum field theory investigations while the methods used to solve them come from pure mathematics. This sort of traditional interaction of physics and mathematics is however coloured by a recent converse phenomenon which makes this interplay truely two-sided and exciting: during the course of the past three decades it often turned out that revolutionary new ideas of quantum physicists were applicable in settling classical open problems of pure geometry, analysis, etc. and even led to the discovery of previously unseen, fully new phenomena in pure mathematics on the other hand. A striking example of this converse interaction is the discovery of exotic differentiable structures on the four dimensional space, probably the most surprising result in calculus since I. Newton. Therefore while E. Wigner wondered about the inexplicable effectivity of mathematics in physical sciences eighty years ago we can do exactly the same nowadays about the inexplicable effectivity of physics in mathematical sciences.

Here I would like to outline my research, regarded as a modest activity in the field outlined above, in four items as follows:

These are the four main areas in which I would like to keep on working in the forthcoming years. It is certainly clear by now that these questions are indeed situated at the common borderline of mathematics and theoretical physics. However I also should emphasize that, beyond these questions, I am always open to other interesting problems, too.


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