## 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

Tuesday, December 18, 2012 — 10:00 AM EST

Monday, December 17, 2012 — 10:00 AM EST

Given natural numbers $n$ and $k$, with $n>k$, the Prouhet-Tarry-Escott (\textsc{pte}) problem asks for distinct subsets of $\mathbb{Z}$, say $X=\{x_1,\ldots,x_n\}$ and $Y=\{y_1,\ldots,y_n\}$, such that

\[x_1^i+\ldots+x_n^i=y_1^i+\ldots+y_n^i\] for $i=1,\ldots,k$. Many

partial solutions to this problem were found in the late 19th century and early 20th century.

Friday, December 7, 2012 — 3:00 PM EST

I will define a slick method to compute the homotopy groups of a finite reflexive digraph and then use the method to show that a motley collection of such digraphs have a nontrivial homotopy group. (Hence by Larose’s Theorem, they do not support Taylor operations.)

Please note date and time.

Friday, December 7, 2012 — 2:00 PM EST

Monday, December 3, 2012 — 4:00 PM EST

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.