Oct

5

Thu

Title: Borel Determinacy I

Speaker: Umar Gaffar

We’re going through Ross Bryant’s presentation of Martin’s theorem (in ZFC) that Borel games are determined.

Nov

30

Thu

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.

Dec

7

Thu

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.

## University of Hawaiʻi at Mānoa