## 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

Friday, November 30, 2012 — 3:30 PM EST

Motivated from the Fuglede conjecture and the discovery of exponential

orthonormal basis on the one-fourth Cantor measure, but not for the

one-third one, there has been interest in understanding the kind of

measures that admit some exponential type bases and their relatives such

as Fourier frames and Riesz bases. By decomposing the measure into

Thursday, November 29, 2012 — 4:30 PM EST

Thursday, November 29, 2012 — 3:30 PM EST

Since Bhargava and Shankar's new method of counting orbits, average orders of the 2,3,4,5-Selmer groups of elliptic curves over Q have been obtained. In this talk we will look at a construction of torsors of Jacobians of hyperelliptic curves using pencils of quadrics and see how they are used to compute the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves over Q with a rational (non-)Weierstrass point.

Thursday, November 29, 2012 — 2:30 PM EST

Putting together some of the machinery developed this term, I will prove Larose’s Theorem: if X is a ﬁnite, connected reﬂexive digraph and X admits a Taylor operation, then for every k ≥ 1, the k-th homotopy group of X is trivial.

Thursday, November 29, 2012 — 11:00 AM EST

Monday, November 26, 2012 — 4:00 PM EST

In this talk, I will describe a new model for describing certain sets S of rational numbers using finite automata. We will see that it is decidable if every element of S is an integer, and that sup S is computable. However, closely related questions are still open. There are applications to combinatorics on words.

Refreshments will be served in MC 5046 at 3:30pm. All are welcome.

Friday, November 23, 2012 — 3:30 PM EST

Thursday, November 22, 2012 — 3:30 PM EST

Abstract: Given natural numbers n and k, the Prouhet-Tarry-Escott (PTE)

asks for integers x_1,..,x_n and y_1,...,y_n such that the sums of the

first k powers are equal. This problem has connections to combinatorics

and theoretical computer science, as well as to other areas of number

Thursday, November 22, 2012 — 2:30 PM EST

Wednesday, November 21, 2012 — 3:30 PM EST

Friday, November 16, 2012 — 3:30 PM EST

Abstract: For a locally compact group $G$, Yin-Hei Cheng considered the closed subspace $a_0(G)$ which is generated by the pure positive definite

Thursday, November 15, 2012 — 2:30 PM EST

Abstract: Two weeks ago, we defined a digraph $F^k(X,x_0)$, whose vertices were a particular set of homomorphisms, and a group $\sigma_k(X,x_0)$, whose elements were connected components of $F^k(X,x_0)$. This week, we will begin looking at these structures in more detail.

Monday, November 12, 2012 — 4:00 PM EST

Friday, November 9, 2012 — 3:30 PM EST

Wednesday, November 7, 2012 — 3:30 PM EST

Friday, November 2, 2012 — 3:30 PM EDT

Thursday, November 1, 2012 — 2:30 PM EDT

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.