Speaker : Michael Yampolsky (University of Toronto)

Title : Computability of Julia sets.

Abstract : Informally speaking, a compact set in the plane is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. Julia sets are some of the best-known mathematical images, however, the questions of their computability and computational complexity are surprisingly subtle. I will survey joint results with M. Braverman and others on computability and complexity of Julia sets.

This semester the Logic Seminar continues at a new day and time, Fridays at 2:30 in Keller 314.

For the first meeting this Friday I will (probably) speak about _Skolem polynomials_:

Abstract:
Over 100 years ago Hardy proved that a certain large class of real functions
was linearly ordered by eventual domination. In 1956 Skolem asked
whether the subclass of integer exponential polynomials is *well*-ordered
by the Hardy ordering, and conjectured that its order type
is epsilon_0. (This class is the smallest containing 1, x, and closed
under +, x, and f^g.) In 1973 Ehrenfeucht proved that the class is
well-ordered, and since then there has been some progress on the order
type.

The proof of well-ordering is rather remarkable and very short, and I
will attempt to expose it (which is to say, cover it) in the hour.

David Ross

Mushfeq Khan will speak on amenability and symbolic dynamics.
As usual the seminar is in Keller 314.

Continuing the theme of symbolic dynamics, I will demonstrate a proof of Simpson’s result that “Entropy = Dimension” for N^d and Z^d, and discuss some of Adam Day’s work generalizing these results to amenable groups.

This week Umar Gaffar will give Shelah’s proof of the following result:

Let $\lambda$ be the cardinality of an ultraproduct of finite sets. If $\lambda$ is infinite then $\lambda=\lambda^{\aleph_0}$.