David Webb will present a new notion of effective dimension, inescapable dimension, which is in a sense dual to complex packing dimension.
The latter was introduced by Freer and Kjos-Hanssen in 2013 in the context of trying to show that the reals of effective Hausdorff dimension 1 are not Medvedev above the bi-immune sets.
Webb will show that the two notions are incomparable, among other results.
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_:
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
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.