## Málstofa í tvinnfallagreiningu 2017

This is the schedule of the Complex Analysis Seminar for 2017:

### Evgeny Poletsky: Bounded psh functions on unbounded domains (joint work with N. Shcherbina)

Friday, 30. June, 10:00-11:30, Tgv227 in Tæknigarður.

Abstract: We will start with manifolds where all bounded psh functions are constants and present the criterion of Rosay for such manifolds. Then we will discuss S-manifolds introduced by Stoll. These manifolds have a psh exhaustion function that is maximal outside of a compact set and we will prove the result of Aytuna and Sadullaev that all bounded psh functions are constants on such manifolds.

After that we will move to the recent results of Harz, Shcherbina and Tomassini who were interested when smooth bounded psh function cannot separate point on a domain $$\Omega$$ in $$\mathbb C^n$$\$. For this they introduced the notion of the core that is the set of points $$z$$ in $$\Omega$$ where there is no a smooth bounded psh function strictly psh near $$z$$. As it happens all bounded psh functions are constant on this set but it can be very wild.

The rest of the talk will be devoted to the HShchT-problem for general psh functions. There the core is related to the Green function and some other objects. You will not be bored.

### Ragnar Sigurðsson:

Friday, 23. June, 10:00-11:30, Tgv227 in Tæknigarður.

Abstract:

### Severine Biard: Compactness estimates for the complex Green operator

Friday, 13. January, 10:00-11:30, Tgv227 in Tæknigarður.

Abstract: I will talk about a sufficient condition, denoted $$(P_q)$$ for the compactness of the complex Green operator of (for smooth pseudoconvex compact CR submanifolds of hypersurface type. I will give the idea of the proof as well.

### Sylvain Arguillère: Sub-riemannian geometry and connections with CR geometry

Friday, 6. January, 10:00-11:30, Tgv227 in Tæknigarður.

Abstract: Sub-Riemannian geometry is the study of non-holonomic constraints in sub-Riemannian manifolds. I will give a brief overview of the main results of sub-Riemannian geometry, while establishing links with CR manifolds of hyper surface type and the $$\overline \partial_b$$ operator.