## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, December 1, 2022 — 10:30 AM EST

**Xinyue (Cynthia) Xie & Layth Al-Hellawi, Department of Pure Mathematics, University of Waterloo **

**"Effectiveness properties of the Walker's Cancellation Theorem - Part IV"**

This is part IV of a series of 4 talks in which we present and build upon the work in Deveau's PhD thesis and examine Walker's Cancellation Theorem from a computability theory perspective. We will continue our investigation of the function *F* which, given the index for a computable group *E:= A ⊕ G = B ⊕ H*, where *A ≅ B* are cyclic and the indices for computable relations determining* A, B, G* and *H*, outputs an index for a computable isomorphism between *G* and *H*. From the previous talks, we know that regardless of whether the generators *a* and *b* of the groups *A* and *B* are given to *F* as inputs, we have *∅ < _{T} F ≤_{T} ∅'*. In this final talk, we will focus on the open question of whether

MC 5417

Event tags

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.