Date 
Speaker 
Title 

Sept 12 
everyone 
Open problem session 
at noon
in C756


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.


Sept 19 
Hadi Kharaghani 
The Strongly Regular Graph SRG$\boldsymbol{(765,192,48,48)}$ 
at noon
in C756

(University of Lethbridge)

Andries Brouwer is 65 and a special issue of Designs, Codes and Cryptography is issued to celebrate the occasion.
Professor Brouwer maintains an elegant public database of existence results for all possible strongly regular graphs on $n\le 1300$
vertices. In a very nice paper, Cohen and Pasechnik implemented most of the graphs listed there in the open source software
Sagemath and obtained a graph for each set of parameters mentioned in the database. In their initial version
of the paper, they mentioned 11 cases as missing values. A number of the cases were related to
my work with professors Janko, Tonchev, and Ionin. I tried to help out with these cases and four cases
were resolved quickly, after I sent detailed instructions. However, there was a problem with the
case of SRG$(765,192,48,48)$. This talk relates to this special case and a nice application of
generalized Hadamard matrices.
To make the talk accessible to general audiences, I will provide many examples illustrating
the concepts involved.


Sept 26 
Farzad Aryan 
On the zero free region of the Riemann zeta function 
at noon
in C756

(Université de Montréal)

We discuss the possibility that the Riemann zeta function has a zero
$\sigma +iT$ to the left of the classical zero free region. We will
show how the existence of this zero forces the function to have many
more zeros in the vicinity of $\sigma+iT$ or/and $\sigma +2iT$.


Oct 3 
Dave Morris 
Hamiltonian paths in projective checkerboards 
at noon
in C756

(University of Lethbridge)

Place a checker in some square of an $m \times n$ rectangular checkerboard,
and glue opposite edges of the checkerboard to make a projective plane.
We determine whether the checker can visit all the squares of the checkerboard
(without repeating any squares), by moving only north and east. This is joint
work with Dallan McCarthy, and no advanced mathematical training will be needed
to understand most of the talk.


Oct 17 
Mikhail Muzychuk 
Noncommutative association schemes of rank $\boldsymbol6$ 
at noon
in C756

(Netanya Academic College, Israel)

An association scheme is a coloring of a complete graph satisfying certain regularity conditions.
It is a generalization of groups and has many applications in algebraic combinatorics. Every association
scheme yields a special matrix algebra called the BoseMesner algebra of a scheme. A scheme is called
commutative if its BoseMesner algebra is commutative. Commutative schemes were the main topic of the
research in this area for decades. Only recently noncommutative association schemes attracted the attention
of researchers. In my talk I'll present the results about noncommutative association schemes of the
smallest possible rank, rank $6$. This is a joint work with A. Herman and B. Xu.


Oct 24 
Nathan Ng 
The sixth moment of the Riemann zeta function and ternary additive divisor sums 
at noon
in C756

(University of Lethbridge)

Hardy and Littlewood initiated the study of the $2k$th moments of the Riemann zeta function
on the critical line. In 1918 Hardy and Littlewood established an asymptotic formula for the
second moment and in 1926 Ingham established an asymptotic formula for the fourth moment.
In this talk we consider the sixth moment of the zeta function on the critical line. We show
that a conjectural formula for a certain family of ternary additive divisor sums implies an
asymptotic formula for the sixth moment. This builds on earlier work of Ivic and of ConreyGonek.


Oct 31 
Amir Akbary 
Valuedistribution of quadratic $\boldsymbol{L}$functions 
at noon
in C756

(University of Lethbridge)

We describe a theorem of M. Mourtada and V. Kumar Murty on the distribution of values
of the logarithmic derivative of the $L$functions attached to quadratic characters.
Under the assumption of the generalized Riemann Hypothesis they prove the existence
of a density function that gives the distribution of values of the logarithmic derivative
of such $L$functions at a fixed real point greater than 1/2. Following classical results
of Wintner, we also describe how this distribution can be described as an infinite
convolution of local distributions.


Nov 14 
Alia Hamieh 
ValueDistribution of Cubic $\boldsymbol{L}$functions 
at noon
in C756

(University of Lethbridge)

In this talk, we describe a method for studying the valuedistribution
of $L$functions based on the JessenWintner theory. This method has
been explored recently by Ihara and Matsumoto for the case of
logarithms and logarithmic derivatives of Dirichlet $L$functions of prime
conductor and by Mourtada and V. K. Murty for the case of logarithmic derivatives
of Dirichlet $L$functions associated with quadratic characters. We show how to
extend such results to the case of cubic characters. In fact, we describe a
distribution theorem for the values of the logarithms and logarithmic derivatives
of a certain family of Artin $L$functions associated with cubic Hecke characters.
This is a joint work with Amir Akbary.


Nov 21 
Luke Morgan 
Permutation groups and graphs 
at noon
in C756

(University of Western Australia)

The use of graphs to study permutation groups goes back to Higman who first
introduced the orbital graphs, and used them to characterise the primitive groups.
Since then, graph theory and permutation group theory have become intertwined,
with many beautiful results. In this talk, I will discuss some problems which
lie across the boundary of permutation group theory and graph theory (or at
least algebraic graph theory), such as how to characterise a new class of
permutation groups that includes the primitive ones  the so called
semiprimitive groups.


Nov 28 
Gabriel Verret 
Vertexprimitive digraphs having vertices with almost equal neighbourhoods 
at noon
in C756

(University of Auckland, New Zealand)

A permutation group $G$ on $\Omega$ is transitive if for every $x, y\in\Omega$ there exists
$g\in G$ mapping $x$ to $y$. The group $G$ is called primitive if, in addition, it preserves
no nontrivial partition of $\Omega$. Let $\Gamma$ be a vertexprimitive digraph, that is,
its automorphism group acts primitively on its vertexset. It is not hard to see that, in
this case, $\Gamma$ cannot have two distinct vertices with equal neighbourhoods, unless
$\Gamma$ is in some sense trivial. I will discuss some recent results about the case when
$\Gamma$ has two vertices with "almost" equal neighbourhoods, and how these results were
used to answer a question of Araújo and Cameron about synchronising groups. (This is joint
work with Pablo Spiga.)

