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 procedure)
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 procedure)
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 procedure)
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: No talk this week
Venue (Same procedure)
Tile:
Abstract:
March 7 13:00.
Speaker: Erik Løw
Venue (Same procedure)
Tile: Polynomial complete vector fields and automorphisms.
Abstract: A survey
March 14 13:00.
Speaker: Tuyen Truong
Venue (Same procedure)
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 procedure)
Tile: Examples of non-rigid actions on manifolds
Abstract: Lattices enjoy many rigidity phenomena for actions on manifolds. Many global and local rigidity results of group actions have been obtained in recent years. In this talk, we will explore the non-rigid aspect of group actions. Focus will be on actions of lattices and fundamental groups of non-positively curved manifolds. This talk is based on joint works with C. Connell, M. Islam, R. Spatzier.