January 25, 13:00.
Speaker: Erlend F. Wold
Venue (We meet in the i 7th floor to find a room, it is difficult to find a room that works all semester)
Titlel: Oka complements
Abstract: We will start by giving some basics about Oka manifolds. Then we will give a “simple” proof of a recent breakthrough result by Kusakabe saying that the complement of (polynomially) convex compact sets in C^n, n\geq 2, are Oka manifolds. This is joint work with Franc Forstneric.
February 1 13:00.
Venue (Same preocedure)
Speaker: Ole Brevig
Title: Backward shift on Hardy spaces
Abstract: Let $S$ denote the forward shift and $B=S^\ast$ the backward shift on the sequence space $\ell^2$. Due to a celebrated result of Beurling on the invariant subspaces of $S$, it is natural to let $S$ and $B$ act on certain spaces of analytic functions in the unit disc. After a gentle introduction, we discuss the following problem: What is the norm on $B$ on the Hardy spaces $H^p$?
Based on joint work with Kristian Seip.
February 8 13:00.
Speaker: Mi Hu
Venue (Same preocedure)
Tile: Improvement of Newton's Method
Abstract: I will discuss an improvement of Newton's method which was created by T. T. Truong. The main advantage of his method (Backtracking New Q-Newton's (BNQN) method) is that the boundary of the basins of the roots seems smooth in the numerical experiments. In this talk, I will present mathematically rigorous proof that for holomorphic polynomials of degree two, the basins of the roots have indeed smooth boundaries.
February 15 13:00.
Speaker: Erlend F. Wold
Venue (Same preocedure)
Tile: Oka properties of complements of complements of closed convex sets in C^n.
Abstract: From recent breakthroughs by Y. Kusakabe much is known about Oka properties of complements of (polynomially) convex compact sets in C^n. In this talk we will give results in the case of non-compact sets. This is joint work with Franc Forstneric.
February 22 13:00. Winter break
February 29 13:00.
Speaker: Erik Løw
Venue (Same preocedure)
Tile: TBA
Abstract: TBA
March 7 13:00.
Speaker: TBA
Venue (Same preocedure)
Tile: TBA
Abstract: TBA
March 14 13:00.
Speaker: Tuyen Truong
Venue (Same preocedure)
Tile: Image of dominant endomorphisms of affine space
Abstract: Chevalley's theorem says that if f: A^n -> A^n is a dominant algebraic map, then A^n\f(A^n) is a constructible set. Can we say more, for example which closed algebraic subvariety W of A^n can be of the form A^n\f(A^n)? (Algebraic) Oka theory has provided a lot evidences towards the conjecture that indeed all subvarieties of codimension at least 2 will be of this form. This talk, joint work with Viktor Balch Barth, proves the following: for any W of codimension at least 2, there is an f such that A^n\f(A^n) is a closed algebraic subvariety of A^n which is birationally equivalent to W.
March 21 13:00.
Speaker: Thang Nguyen
Venue (Same preocedure)
Tile: TBA
Abstract: TBA