Groups in Galway 2018
May 1819, 2018
Groups in Galway has been running on an annual basis since 1978.
The scope of the conference covers all areas of group theory,
applications, and related fields. All
who are interested are invited to attend.
Speakers
The speakers are

Rob Craigen (Manitoba)

Ronan Egan (Rijeka)

Bettina Eick (Braunschweig)

Daniel Horsley (Monash)

Eoin Long (Oxford)

Maura Paterson (Birbeck)

Götz Pfeiffer (Galway)

John Sheekey (UCD)

Ann Trenk (Wellesley)
Schedule
Below is a tentative schedule.
All talks will be in
AC201 on the concourse of the Arts/Science Building (number 14 on this
map).
Move the cursor over a title for the talk's abstract.
Friday 18 May
10.00‒10.45
John Sheekey
Semifields and subspaces of matrices over finite fields
Finite semifields are nonassociative division algebras over a finite field. They have been studied since the early 1900s, with Dickson constructing the first nontrivial examples. The theory was further developed by Albert and Knuth in the 1960s.
Semifields correspond to various objects in both linear algebra and finite geometry. They correspond for example to a certain class of projective plane; certain types of spreads in a projective space $\mathrm{PG}(2n1,q)$; nonsingular tensors in $\mathbb{F}_q^n\otimes \mathbb{F}_q^n\otimes \mathbb{F}_q^n$; and $n$dimensional subspaces of $n\times n$ matrices in which every nonzero element is invertible. The last of these is of particular recent interest, as this is a special case of a maximum rank distance (MRD) code, a hot topic due to potential applications in network coding.
We will provide an overview for these connections, the known constructions and classifications, and present some open problems in the area.
10.45‒11.30
Coffee/tea
11.30‒12.15
Eoin Long
Recent results on set intersections
The study of set intersections forms a popular topic of research in extremal combinatorics, and has a wide range of applications to different areas of mathematics. Roughly speaking, here one aims to understand how large a collection of sets can be subject to a restriction on the pairwise intersections of its elements. In this talk I will discuss some recent progress on problems of this type. Joint work with Peter Keevash.
12.30‒13.15
Maura Paterson
Reciprocallyweighted external difference families
Let $G$ be a finite abelian group of order $n$. An $(n,k,\lambda)$ $m$External Difference Family (EDF) is a collection of $m$ disjoint subsets of $G$ each of size $k$, with the property that each nonzero group element occurs precisely $\lambda$ times as a difference between group elements in two different subsets from the collection. A reciprocallyweight EDF (RWEDF) is a generalisation of an EDF in which the subsets may have different sizes, and the differences are counted with a weighting given by the reciprocal of the set sizes. These were proposed in connection with the study of weak algebraic manipulation detection codes. In this talk I will motivate the definition of RWEDFs before discussing recent results including the construction of infinite families of RWEDFs.
13.15‒14.30
Lunch
14.30‒15.15
Daniel Horsley
Symmetric coverings and the BruckRyserChowla theorem
A $(v,k,\lambda)$block design is a collection of $k$element subsets, called blocks, of a $v$set of points such that each pair of points appears together in exactly $\lambda$ blocks. A block design is symmetric if it has exactly as many blocks as points. The BruckRyserChowla theorem famously establishes the nonexistence of various symmetric block designs, including projective planes.
In this talk I will discuss generalisations of the BruckRyserChowla theorem to the setting of coverings where, instead of demanding that each pair of points appears together in exactly some fixed number of blocks, we only require that each pair of points appear together in at least some fixed number of blocks. The proofs of these generalisations exploit the structure of $XX^T$, where $X$ is the incidence matrix of a putative covering. In some cases it is sufficient to examine the determinants of these matrices. In others, arguments concerning rational congruence of matrices and making use of HasseMinkowski invariants are required.
15.30‒16.15
Bettina Eick
The groups of order $p^n q$
The talk shows how the number $f_n(p,q)$ of groups of order
$p^n q$ for different primes $p$ and $q$ can be determined (for
fixed $n$ as a function in $p$ and $q$). Explicit functions for $f_n$
for $n \leq 5$ are exhibited.
16.15‒17.00
Coffee/tea
17.00‒17.45
Götz Pfeiffer
TBA
TBA
19.00
Conference Dinner
Saturday 19 May
10.00‒10.45
Ronan Egan
Using groups to construct combinatorial structures and codes
In this talk I will discuss methods of constructing combinatorial structures such as block designs from finite groups and using orbit matrices. I will also describe recent and ongoing work where generalized versions of orbit matrices are constructed from Hadamard matrices and weighing matrices using their permutation automorphism groups. This leads to the construction of selforthogonal, selfdual, optimal and near optimal codes over finite fields.
10.45‒11.15
Coffee/tea
11.15‒12.00
Rob Craigen
TBA
TBA
12.15‒13.00
Ann Trenk
The distinguishing chromatic number and NGgraphs
Albertson and Collins introduced the distinguishing number of a graph as the minimum number of colors needed to color the vertices so that the only automorphism of the graph which preserves colors is the identity. The distinguishing chromatic number, $\chi_D(G)$, is defined similarly, except that the coloring must also be proper, that is, adjacent vertices must get different colors. In this talk we discuss results about $\chi_D(G)$ including characterization theorems and connections to the NordhausGaddum inequality for graphs.
Registration
There is no registration fee. However, if you intend to participate in the
conference, please send an email to the organizers Kevin Jennings and Dane Flannery, stating your full name, affiliation, and whether you will attend the Dinner.
Travel
Galway can be reached by public transportation from Dublin, Shannon, and Knock
airports. There are direct buses from Dublin airport to Galway city
operated by
Citylink
and
GoBus. You can also take a
train from Dublin city.
Bus Eireann
runs buses from Dublin, Shannon, and Knock airports to Galway.
Directions to NUI Galway by road can be found
here.
Galway is a small city. It takes about 15 minutes to walk from the Coach Station or Railway Station to the university (
Google maps direction).
NUI Galway has a number
of
payanddisplay
parking places for visitors. Cars parked in other spaces on the NUI
Galway campus and not displaying a valid parking permit will be
clamped.
Accommodation
The following hotels and guest houses are convenient for the NUI Galway campus:
 The Westwood House Hotel,
091 521442
 The House Hotel,
091 538900
 Bologna B&B, 091 523792
 Aneesha B&B, 091 524250
 Ashgrove House B&B, 091 581291
 Villanova B&B, 091 524849
 Coolavalla B&B, 091 522415
 Rosgal B&B, 091 524723
 De Sota B&B, 091 585064
See also Discover Ireland.
For further information, contact Kevin Jennings
or Dane Flannery.
Groups in Galway 2018 is supported by