Date 
Speaker 
Title 

Sep 11 
everyone 
Open problem session 
at noon
in C630


Please bring your favourite
(math) problems. Anyone with a problem to share will be given
about 5 minutes to present it. We will also choose most of the
speakers for the rest of the semester.


Sep 18 
PengJie Wong 
Nearly supersolvable groups and Artin's conjecture 
at noon
in C630

(University of Lethbridge)

Let $K/k$ be a Galois extension of number fields with Galois group $G$, and let $\rho$ be a nontrivial irreducible representation of $G$ of dimension $n$. The Artin holomorphy conjecture asserts that the Artin $L$function attached to $\rho$ extends to an entire function.
It is wellknown that when $n=1$, this conjecture follows from Artin reciprocity. Also, by the works of Langlands and many others, we know that this conjecture is valid for $n=2$ under certain conditions. However, in general, the Artin holomorphy conjecture is wildly open.
In this talk, we will discuss how elementary group theory plays a role in studying the Artin holomorphy conjecture and introduce the notion of "nearly supersolvable groups". If time allows, we will explain how such groups lead to a proof of the Artin holomorphy conjecture for Galois extensions of degree less than 60.


Sep 25 
Muhammad Khan 
The contact graphs of totally separable packings 
at noon
in C630

(University of Lethbridge)

Contact graphs have emerged as an important tool in the study of translative packings
of convex bodies and have found numerous applications in materials science. The
contact number of a packing of translates of a convex body is the number of edges
in the contact graph of the packing, while the Hadwiger number of a convex body is
the maximum vertex degree over all such contact graphs. In this talk, we investigate
the Hadwiger and contact numbers of totally separable packings of convex bodies, known
as the separable Hadwiger number and the separable contact number, respectively. We
show that the separable Hadwiger number of any smooth strictly convex body in dimensions
$d = 2, 3, 4$ is $2d$ and the maximum separable contact number of any packing of $n$
translates of a smooth strictly convex domain is $\lfloor 2n  2\sqrt{n} \rfloor$. Our
proofs employ a characterization of total separability in terms of hemispherical caps
on the boundary of a smooth convex body, Auerbach bases of finite dimensional real
normed spaces, angle measures in real normed planes, minimal perimeter polyominoes
and an approximation of smooth $o$symmetric strictly convex domains by, what we call,
Auerbach domains. This is joint work with K. Bezdek (Calgary) and M. Oliwa
(Calgary).


Oct 2 
Andrew Fiori 
The average number of quadratic Frobenius pseudoprimes 
at noon
in C630

(University of Lethbridge)

Primality testing has a number of important applications. In particular in
cryptographic applications the complexity of existing deterministic algorithms
causes increasing latency as the size of numbers we must test grow and the
number of tests we must run before finding a prime grows aswell. These
observations lead one to consider potentially nondeterministic algorithms
which are faster, and consequently leads one to consider the false positives
these algorithms yield, which we call pseudoprimes.
In this talk I will discuss my recent work with Andrew Shallue where we study Quadratic
Frobenius Pseudoprimes. I shall describe our results on an asymptotic lower bounds on
the number of false positives. These results represent a generalization of those
ErdosPomerance concerning similar problems for (Fermat) pseudoprimes.


Oct 16 
Lee Troupe 
Title TBA 
at noon
in C630

(University of British Columbia)

Abstract TBA


Oct 23 
Sam Broadbent, Kirsten Wilk, and Habiba Kadiri 
Title TBA 
at noon
in C630

(University of Lethbridge)

Abstract TBA


Oct 30 
Akshaa Vatwani 
Title TBA 
at noon
in C630

(University of Waterloo)

Abstract TBA


Nov 6 
Forrest Francis 
Title TBA 
at noon
in C630

(University of Lethbridge)

Abstract TBA


Nov 20 
Kirsty Chalker 
Title TBA 
at noon
in C630

(University of Lethbridge)

Abstract TBA


Nov 27 
Sara Sasani 
Title TBA 
at noon
in C630

(University of Lethbridge)

Abstract TBA


Dec 4 
Joy Morris 
Title TBA 
at noon
in C630

(University of Lethbridge)

Abstract TBA

