We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale.  Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

Explore the geometry and symmetries of surfaces and other mathematical objects and explore their relevance in physical, chemical and biological contexts. 

The aim of this project is to introduce quantum integrable systems which play a very important role in modern theoretical physics. Such systems provide one of very few ways to analyze nonlinear effects in continuous and discrete quantum systems.

We apply the most advanced quantum-mechanical modeling to resolve electron motion in atoms and molecules on the atto-second (one quintillionth of a second) time scale.  Our theoretical modeling, based on a rigorous, quantitative description of correlated electron dynamics, provides insight into new physics taking place on the atomic time scale.

A range of projects are available applying and developing the tools of topological data analysis. Data include 2D and 3D images, structural motifs in molecular-dynamics simulations, and porous materials. 

Explore the geometry and symmetries of surfaces and other mathematical objects and explore their relevance in physical, chemical and biological contexts. 

There are many interesting physical statistical systems which never reach thermal equilibrium. Examples include surface growth, diffusion processes or traffic flow. In the absence of general theory of such systems a study of particular models plays a very important role. Integrable systems provide examples of such systems where one can analyze time dynamics using analytic methods.

The project studies possibility of the coherent control (i.e. manipulating properties of a quantum system, such as charge density, levels populations, etc., using a suitably tailored laser pulse) for a quantum mechanical model of a molecule.

Using methods of quantum many-body theory to describe elementary processes in atoms and molecules interacting with strong electromagnetic fields.

Periodic frameworks, viewed as simple mechanisms, can be rigid or display a variety of exotic deformation properties such as surface modes or expansive auxetic motion. This project will conduct a systematic search for frameworks with these properties. 

What are the underlying geometric and topological properties of periodic structures that guarantee large and stable porosity in nano-porous crystalline materials required for gas storage and efficient catalysis?

In recent years there was a large boost in development of advanced variational methods which play an important role in analytic and numerical studies of  1D and 2D quantum spin systems. Such methods are based on the ideas coming from the renormalization group theory which states that  physical properties of  spin systems become scale invariant near criticality. One of the most powerful variational algorithms is the corner-transfer matrices (CTM) method which allows to predict properties of large systems based on a simple iterative algorithm.

We will study links between integrable systems in statistical mechanics, combinatorial problems and special functions in mathematics. This area of research has attracted many scientist's attention during the last decade and revealed unexpected links to other areas of mathematics like enumeration problems and differential equations.

A range of projects are available applying and developing the tools of topological data analysis. Data include 2D and 3D images, structural motifs in molecular-dynamics simulations, and porous materials. 

Periodic frameworks, viewed as simple mechanisms, can be rigid or display a variety of exotic deformation properties such as surface modes or expansive auxetic motion. This project will conduct a systematic search for frameworks with these properties. 

What are the underlying geometric and topological properties of periodic structures that guarantee large and stable porosity in nano-porous crystalline materials required for gas storage and efficient catalysis?