Wednesday, December 2, 2015 — 3:30 PM EST

**Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo **

We will show that the notion of Schnorr randomness is consistent with intuition and leads to the desired statistical properties of random sets. Also we will prove the nice facts we have stated about the Schnorr test.
Wednesday, December 2, 2015

MC 5479

**Please Note Room**

Wednesday, November 25, 2015 — 3:30 PM EST

**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

Wednesday, November 18, 2015 — 3:30 PM EST

**Michael Deveau, Department of Pure Mathematics, University of Waterloo **

Wednesday, November 11, 2015 — 3:30 PM EST

**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

Wednesday, October 28, 2015 — 3:30 PM EDT

**Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo **

Wednesday, October 21, 2015 — 3:30 PM EDT

**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.

Wednesday, October 14, 2015 — 3:30 PM EDT

**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.

Wednesday, October 14, 2015 — 2:30 PM EDT

**David McKinnon, Department of Pure Mathematics, University of Waterloo**

“S-arithmetic groups and quantum computing”

Tuesday, October 13, 2015 — 11:30 AM EDT

**Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo **

“Prime and semiprime rings”

Tuesday, September 22, 2015 — 2:30 PM EDT

Juan Felipe Carmona, Universidad Antonio Nariño

"Flatness and CM-triviality in strongly minimal theories with a predicate"

Wednesday, September 16, 2015 — 3:30 PM EDT

**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.

Thursday, August 27, 2015 — 2:00 PM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo **

We finish the proof that the non-distributive lattice M5 can be embedded into the c.e. degrees, picking up with where we left off last week: the verification that the minimal pair condition holds pairwise for A1, A2andA3.

Thursday, August 20, 2015 — 2:00 PM EDT

Michael Deveau, Department of Pure Mathematics, University of Waterloo

We continue with the proof that the non-distributive lattice M5 can be embedded into the c.e. degrees. We will begin with a somewhat brief reminder of the details of the construction presented last week by Jonny, and then begin work on the verification of the construction to show that it gives the desired result.
MC 5403

Thursday, August 6, 2015 — 2:00 PM EDT

**Jonny Stephenson, Pure Mathematics, University of Waterloo**

The question of which finite lattices can be embedded into the c.e.

degrees first arose with the construction of a minimal pair by Yates,

and independently by Lachlan, showing the 4 element Boolean algebra

can be embedded. This result was rapidly generalised to show any

finite distributive lattice can also be embedded. For non-distributive

lattices, the situation is more complicated.

Thursday, July 23, 2015 — 2:00 PM EDT

**Mohammad Mahmoud, Pure Mathematics, University of Waterloo**

We continue to show that the class Kw has no Turing Ordinal. We construct a set D which is not enumeration reducible to R_\A for any structure \A in Kw. This will imply directly that if the Turing ordinal exists then it must be strictly greater than 0. On the other hand Joe Miller showed that, for our class, if the Turing Ordinal exists it must be 0. Both statements tell us that the Turing Ordinal can't exist.

Thursday, July 16, 2015 — 2:00 PM EDT

**Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo **

We present the notion of Turing Ordinal of a class of structures. The Turing Ordinal was introduced by Jockusch and Soare as a computability theoretic method for comparing complexities of classes of structures. We explain an example by Montalban of a class of structures that doesn’t have a Turing Ordinal.
M3 4206

Thursday, June 25, 2015 — 2:00 PM EDT

**David Belanger, Cornell University**

Thursday, June 18, 2015 — 2:00 PM EDT

**Russell Miller, Queens College - City University of New York **

Thursday, June 11, 2015 — 2:00 PM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo **

Thursday, June 4, 2015 — 2:00 PM EDT

**Russell Miller, Queens College - City University of New York **

Thursday, May 28, 2015 — 2:00 PM EDT

**Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo **

We have seen with Sam two proofs of Ramsey’s Theorem. This time we give a third proof of that uses Konig’s Lemma but can be carried out in RCA0.
M3-4206

Monday, March 30, 2015 — 1:00 PM EDT

**Jason Bell and Rahim Moosa, Department of Pure Mathematics, University of Waterloo **

We wrap up proof of the approximate group theorem.
Monday, March 30, 2015 1:00 pm MC 5479

** Please note Day and Room**

Friday, March 27, 2015 — 12:59 PM EDT

**Sam Eisenstat, Department of Pure Mathematics, University of Waterloo **

Tuesday, March 24, 2015 — 2:30 PM EDT

**Ian Payne, Department of Pure Mathematics, University of Waterloo **

I will talk about a CSP algorithm that works when each potato has a special congruence. That is, the quotient by it is a semilattice, and each block of it is Maltsev (plus a bit more). After that, I’ll talk about some effort to weaken the word semilattice in the previous sentence.
MC 5479

Friday, March 20, 2015 — 1:00 PM EDT

**Rahim Moosa, Department of Pure Mathematics, University of Waterloo **

We continue to follow van den Dries Seminaire Bourbaki article entitled Approximate Groups [after Hrushovski, and Breuillard, Green, Tao]. The subject involves the interaction of additive combinatorics and model theory.
MC 5413