## Mitja Nedić (16/04/15)

Math Colloquium

### Speaker: Mitja Nedić, Stockholm University

Title: q-conevxity

Location: Interactive room, 2 floor in Tæknigarður.

Time: Thursday, April 16, at 11:00-12:00.

### Abstract:

We will begin the talk by recalling the notion of the Levi form and list some of its basic properties. With the help of the Levi form we then define plurisubharmonic functions and show the equivalence of this definition with others. We will also quickly look at some examples and list some properties of plurisubharmonic functions. We will then define the notion of q-convexity in the case of functions, manifolds and bundles and explore some examples and properties.

We list the theorems that connect metric q-convexity of holomorphic bundles with the q-convexity of complex manifolds.

Finally, we state the Morse lemma for plurisubharmonic function and use it to prove the Morse lemma for q-convex functions. If time, we will state the theorems on the CW decomposition of 1-complete and q-complete manifolds and their consequences.