Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
The topic for the Computability Learning Seminar this term will be Algorithmic Random- ness. We will be following Nies’s book, Computability and Randomness.
Juan Felipe Carmona, Universidad Antonio Nariño
"Flatness and CM-triviality in strongly minimal theories with a predicate"
Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
“Prime and semiprime rings”
David McKinnon, Department of Pure Mathematics, University of Waterloo
“S-arithmetic groups and quantum computing”
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
We will continue last week’s discussion of prefix-free Kolmogorov complexity, but will begin to focus more on infinite sequences. We will discuss what we might mean when we say that an infinite sequence looks random from an algorithmic perspective.
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
“Randomness Continued”
Last time we introduced Martin-Lof randomness, and saw that most reals have this prop- erty.
This week, we will give an example of one specific Martin-Lof random real, discuss some of the properties which such reals satisfy, and give another characterization of them.
MC 5403
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
Michael Deveau, Department of Pure Mathematics, University of Waterloo
We continue last week’s presentation and present a proof of van Lambalgen’s Theorem. To conclude this subsection, we also remark on some of the consequences of this result. Time per- mitting, we also discuss some applications of relativized randomness to lowness and highness.MC 5403
Michael Deveau, Department of Pure Mathematics, University of Waterloo
Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
Though Martin-L ̈of randomness is the central randomness notion we have discussed, one can address criticisms to the claim that this notion is the appropriate one by considering weaker and stronger randomness notions for sets. We will discuss weaker variants.
MC 5403