Mathematical Research Seminar
Mathematical research seminar is organized by the departments of Mathematics of two members of the University - UP FAMNIT and Andrej Marušič Institute (UP IAM), every Monday from October to June.
You are cordially invited to attend the lectures.
Kahler manifolds appear naturally in both Algebraic and Differential Geometry: projective complex varieties from Algebraic Geometry, and smooth manifolds with riemannian metrics with holonomy U(n). Understanding when a manifold may admit a Kahler structure and how far it is from that is a key problem in geometry. Classically, tools from global analysis (harmonic forms and Hodge theory) provide striking topological properties of Kahler manifolds, linking topology and analysis. We shall review this circle of ideas, and recent results on the construction of manifolds admitting complex structures (and even both complex and symplectic structures simultaenously) but not admitting Kahler structures.
We shall recall of basic principles of the non-commutative harmonic analysis, discuss the case of classical groups, and how problems of non-commutative harmonic analysis in this case are linked with some important problems of modern theory of automorphic forms.
The electrical activity generated by nerve cells of the brain can be measured through electrodes attached to various locations on the scalp. This technique is known as electroencephalography (EEG) and is helpful not only in clinical work, but also in studying various cognitive processes. In the talk we present how graph theory can be used to analyse EEG data. The efficiency of the graph-theoretical approach is illustrated in the case of a mild cognitive impairment.