Seminar

Rahim Moosa, University of Waterloo

Definable groups in CCM

I will survey what is known about the structure of definable groups in both the standard and nonstandard models of CCM.

MC 5479

William Dan, University of Waterloo

A Characterization of Random, Left C.E. Reals

An immediate property of the halting probability of a prefix-free machine is that it is a left c.e. real. An easycorollary of the Kraft-Chaitin theorem is that the converse is true: any left c.e. real is the halting probability ofsome prefix-free machine. The most common example of a random real is Chaitin's omega, the haltingprobability of a universal prefix-free machine. In fact, it is a random left c.e. real. It is natural then to ask if theconverse holds in this case as well: that any random left c.e. real is the halting probability of some universalprefix-free machine. As it turns out, this is the case, and in this talk I will explain the concept used to solve thisquestion, Solovay reducibility, then prove the theorems demonstrating the converse. This talk follows sections9.1 and 9.2 of the Downey and Hirschfeldt book.

MC 5403

Catherine St-Pierre, University of Waterloo

"Borel fixed Ideals (in Krull dimension 0)"

Kübra Benli, University of Georgia

"On the number of small prime power residues"

Dan Ursu, Department of Pure Mathematics, University of Waterloo

"Relative C* - simplicity"

Rahim Moosa, Pure Mathematics, University of Waterloo

"Pseudo-finite sets and dimension, Part 2"

Having discussed the normalised counting measure on pseudo-finite sets and its application to Szemeredi Regularity, we now introduce the fine and coarse pseudo-finite dimensions for these sets, with an eye toward the Szemerdi-Trotter theorem.

Ross Willard, Pure Mathematics, University of Waterloo

"Natural dualities for finitely generated quasi-varieties - definitions and first results"

Eli Shamovich, Pure Mathematics, University of Waterloo

"Polynomials and rational functions"

Fei Hu, University of British Columbia

"Jordan property for algebraic groups in arbitrary characteristic"

Pranabesh Das, Pure Mathematics, University of Waterloo

"Variants of Erd{\H o}s--Selfridge superelliptic curves and their rational points"