Teaching

During the Winter Semester 2024/25 I teach the Master course Fiber Bundles. More information can be found on the corresponding spletna učilnica page.

Possible Thesis Topics

I am available to supervise a Master's thesis. Possible topics include but are not limited to:

• The density property for Stein manifolds
  The group of bijective holomorphic self-maps (automorphisms) of the complex plane consists only of affine maps. In contrast, complex Euclidean spaces of dimension more than one possess an infinite-dimensional group of automorphisms. This fact (and many others!) is shared among the class of Stein manifolds with the density property. For your thesis, you could learn some aspects of this theory and eventually focus on understanding some recent research on the topic.
• The legacy of Rosay and Rudin
  In 1988, Rosay and Rudin published the paper Holomorphic Maps from Cn to Cn; this is a vast work that has since been used and explored by many different researchers. The student should become familiar with (some of) the topics discussed there, with the aim to later delve into one of the many areas that benefitted from this seminal work.
• The mean-curvature flow
  Consider a surface immersed in 3-dimensional space. To each point of the surface, it is possible to assign the mean-curvature vector; it is proportional to the normal vector, scaled by the mean-curvature of the surface. The mean-curvature flow consists of deforming the initial surface by following its mean-curvature vector; it is deeply connected to minimal surfaces and its understanding requires knowledge of parabolic PDEs. We would begin by studying the general theory of the mean-curvature flow, before deciding on a more specific focus.