# Events

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

## Michael Filaseta, University of South Carolina

### “49598666989151226098104244512918”

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

## Timothy Caley, Pure Mathematics, University of Waterloo

### "The Prouhet-Tarry-Escott problem"

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

## Ross Willard, Department of Pure Mathematics University of Waterloo

### “Applications of Larose’s Theorem”

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.)

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

## Sebastien Guex, University of Alberta

### “Ergodic theorems for certain Banach algebras associated to locally compact groups.”

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

## Malabika Pramanik, University of British Columbia

### "Needles, bushes, hairbrushes and polynomials"

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

## Chun Kit Lai, McMaster University

### "Fourier frames on general measure spaces"

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

## Ian Payne, Pure Mathematics, University of Waterloo

### "I Can't Get No (Constraint) Satisfaction"

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

## Jerry Wang, Harvard University

### "Pencils of quadrics and 2-Selmer groups of Jacobians of hyperelliptic curves"

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

## Ross Willard, Pure Mathematics, University of Waterloo

### "Larose's theorem"

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

## Cassie Naymie, Pure Mathematics, University of Waterloo

### “Roth’s theorem on ﬁnite abelian groups”

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

## Jeffrey Shallit, School of Computer Science, University of Waterloo

### "Rational numbers and automata"

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

## Kai-Cheong Chan, University of Waterloo

### “On tensor products of digraph algebras over pre-ordered groups ”

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

## Timothy Caley, Department of Pure Mathematics, University of Waterloo

### "A new algorithm for the Prouhet-Tarry-Escott problem"

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

## Carrie Knoll, Department of Pure Mathematics,  University of Waterloo

### “Idempotent operations in reflexive digraphs”

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

## Jessie Yang, McMaster University

### Tropical Severi Varieties”

Tuesday, November 20, 2012 — 2:30 PM EST

## Logic seminar

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

## Nico Spronk, Department of Pure Mathematics, University of Waterloo

### "On the subalgebra of a Fourier-Stieltjes algebra generated by pure positive definite functions"

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

## Peter Sinclair, University of Waterloo

### "Auxiliary Results on Homotopy Groups and Digraphs"

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

## Dima Sinapova, University of Illinois, Chicago

### "Powers of singular cardinals"

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

## Mehdi Monfared, University of Windsor

### “Involutions and Trivolutions on Second Dual Algebras”

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

## Graham Denham, Western University

### “Duality properties for abelian covers”

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

## Analysis seminar

### “Algebraic frames”

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

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

### “Continuation of Discrete Homotopy”

I will continue to prove that the operation I defined last week is well defined, and is a group operation. The next step is to define higher homotopy groups, and maybe even do a (very) small example.
Tuesday, October 30, 2012 — 3:30 PM EDT

## Pantelis Eleftheriou, Department of Pure Mathematics, University of Waterloo

### “Model-theoretic constructions in many-valued modal logics”

Monday, October 29, 2012 — 4:00 PM EDT

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