Department of Mathematics

110 Frelinghuysen Road

Hill Center Busch Campus

Rutgers University

Piscataway, NJ, 08854

Office: Hill 210

Phone number: (732) 445-2390 x7002

Email: miroslav@math.rutgers.edu

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature . . . . If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

Try and penetrate with our limited means the secrets of nature and you will find that, behind all the discernible concatenations, there remains something subtle, intangible and inexplicable. Veneration for this force beyond anything that we can comprehend is my religion. To that extent I am, in point of fact, religious.

Nature, however, does not reveal itself in the form of differential equations directly but rather as a point cloud collected by the experimentalists. Today there is a tremendous amount of data but no universal method for understanding it. In my current research, I use methods of algebraic topology and the power of computers to analyze large and potentially high dimensional data sets. An integral part of my research is developing methods that allow a meaningful comparison of experimental and simulated data so that the similarities as well as the differences between them can be better understood.

In order to fully appreciate the dynamical mechanisms of nature we need to treat our data as a time series. We apply topological methods and theory of dynamical systems to study these time series. Often the most interesting dynamics happen in a subset of the space in which the point cloud is embedded. The dimension of this set tends to be much smaller than the dimension of the ambient space. This opens a door for reconstructing the dynamic from the data in a more manageable space. I'm interested in using topological tools such as Conley index to show the existence of fixed points, periodic orbits and other invariant sets hidden in the experimental data.