Přednášky se konají v 17:00 v posluchárně M2 na Janáčkově nám. 2a v Brně, pokud není explicitně uvedeno jinak.

12. října

Dmitri Alekseevsky (Brno)
Quaternionic Geometry

Abstrakt:

The lecture will first offer a short and elementary survey of quaternionic geometry. Then the twistor description of Kaehler submanifolds will be given. In particular, the classification of Kaehler submanifolds of Wolf spaces with the parallel second fundamental form will be discussed.

9. listopadu

Emil Straube (Texas A&M University)
D-bar methods in complex analysis

Abstrakt:

In this talk, we will indicate some typical applications of d-bar methods in complex analysis of one and several variables. We start with the solution of the inhomogeneous d-bar equation in a planar domain, which lends itself to a simple proof of the Weierstrass theorem on holomorphic functions with prescribed zeroes. Next, we describe how one variable methods give the solution of the inhomogeneous Cauchy-Riemann equations in Cn when the right hand side has compact support, and how this simple observation already leads to a phenomenon that is radically different from the one variable case, namely the Hartogs extension theorem. This leads to the question of domains of existence of holomorphic functions, and we indicate how these domains are characterized by the solvability of the inhomogeneous d-bar equations. Finally, we add some remarks about solving the inhomogeneous equations with regularity estimates up to the boundary.