Events

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Wednesday, December 2, 2015

MC 5479

**Please Note Room**

Jonathan Stephenson, Department of Pure Mathematics University of Waterloo

We will start by sketching the weaker implications obtained by relaxing 2-randomness to 3-randomness and 1-randomness. These results give a good idea of the proof strategy used to prove the full theorem.

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

Given a class C of real numbers which can be relativized to a class C(X) depending on a real parameter X, we say that X is low for C if C(X)=C.

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

We will continue our study of the relationships between different lowness notions. Each such notion captures the idea of a real number having minimal computational power according to some criterion.

Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo

We often regard the computational power of a set A as being synonymous with the class of sets A is able to compute. However, we might instead ask which sets are able to compute A. The class of such sets is called the cone above A. When the cone above A consists of few sets, we may think of A as being difficult to compute. We wish to make the term ”few sets” precise.

Alex Kruckman, University of California, Berkeley

Michael Deveau, Department of Pure Mathematics, University of Waterloo

We briefly recall the definition of a base for ML-randomness presented last time. The remaining portion of the talk will be spent stating and proving an important result about such sets, namely that every base for ML-randomness is low for K.

MC 5403

Michael Deveau, Department of Pure Mathematics, University of Waterloo

We first discuss lowness for pairs of randomness notions, and then begin proving the theo- rem mentioned last time: Low(W2R,MLR) = Low(MLR).

MC 5403

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

Last time we have seen an upper bound on the number of K-trivial sets via some constant b. This week we compute a lower bound which as we will see is also a ”tight” bound (close to the exact number).

MC 5403