 SYMMETRY IN NEWCASTLE
 Location: Room V109, Mathematics Building (Callaghan Campus) The University of Newcastle
 Dates: Fri, 2^{nd} Aug 2019  Fri, 2^{nd} Aug 2019

Schedule:
121: Brian Alspach
12: Lunch
23: John Bamberg
33.30: Tea
3.304.30: Marston Conder
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: Honeycomb Toroidal Graphs
 Abstract for Honeycomb Toroidal Graphs:
The honeycomb toroidal graphs are a family of graphs I have been looking at now and then for thirty years. I shall discuss an ongoing project dealing with hamiltonicity as well as some of their properties which have recently interested the computer architecture community.
 Speaker: A/Prof John Bamberg, University of Western Australia
 Title: Symmetric finite generalised polygons
 Abstract for Symmetric finite generalised polygons:
Finite generalised polygons are the rank 2 irreducible spherical buildings, and include projective planes and the generalised quadrangles, hexagons, and octagons. Since the early work of Ostrom and Wagner on the automorphism groups of finite projective planes, there has been great interest in what the automorphism groups of generalised polygons can be, and in particular, whether it is possible to classify generalised polygons with a prescribed symmetry condition. For example, the finite Moufang polygons are the 'classical' examples by a theorem of Fong and Seitz (19731974) (and the infinite examples were classified in the work of Tits and Weiss (2002)). In this talk, we give an overview of some recent results on the study of symmetric finite generalised polygons, and in particular, on the work of the speaker with Cai Heng Li and Eric Swartz.
 Speaker: Prof. Marston Conder, Department of Mathematics, The University of Auckland
 Title: Edgetransitive graphs and maps
 Abstract for Edgetransitive graphs and maps:
In this talk I'll describe some recent discoveries about edgetransitive graphs and edgetransitive maps. These are objects that have received relatively little attention compared with their vertextransitive and arctransitive siblings.
First I will explain a new approach (taken in joint work with Gabriel Verret) to finding all edgetransitive graphs of small order, using single and double actions of transitive permutation groups. This has resulted in the determination of all edgetransitive graphs of order up to 47 (the best possible just now, because the transitive groups of degree 48 are not known), and bipartite edgetransitive graphs of order up to 63. It also led us to the answer to a 1967 question by Folkman about the valencytoorder ratio for regular graphs that are edge but not vertextransitive.
Then I'll describe some recent work on edgetransitive maps, helped along by workshops at Oaxaca and Banff in 2017. I'll explain how such maps fall into 14 natural classes (two of which are the classes of regular and chiral maps), and how graphs in each class may be constructed and analysed. This will include the answers to some 18yearold questions by Širáň,
Tucker and Watkins about the existence of particular kinds of such maps on orientable and nonorientable surfaces.
 Abstract for Honeycomb Toroidal Graphs:
The honeycomb toroidal graphs are a family of graphs I have been looking at now and then for thirty years. I shall discuss an ongoing project dealing with hamiltonicity as well as some of their properties which have recently interested the computer architecture community.
 Abstract for Symmetric finite generalised polygons:
Finite generalised polygons are the rank 2 irreducible spherical buildings, and include projective planes and the generalised quadrangles, hexagons, and octagons. Since the early work of Ostrom and Wagner on the automorphism groups of finite projective planes, there has been great interest in what the automorphism groups of generalised polygons can be, and in particular, whether it is possible to classify generalised polygons with a prescribed symmetry condition. For example, the finite Moufang polygons are the 'classical' examples by a theorem of Fong and Seitz (19731974) (and the infinite examples were classified in the work of Tits and Weiss (2002)). In this talk, we give an overview of some recent results on the study of symmetric finite generalised polygons, and in particular, on the work of the speaker with Cai Heng Li and Eric Swartz.
 Abstract for Edgetransitive graphs and maps:
In this talk I'll describe some recent discoveries about edgetransitive graphs and edgetransitive maps. These are objects that have received relatively little attention compared with their vertextransitive and arctransitive siblings.
First I will explain a new approach (taken in joint work with Gabriel Verret) to finding all edgetransitive graphs of small order, using single and double actions of transitive permutation groups. This has resulted in the determination of all edgetransitive graphs of order up to 47 (the best possible just now, because the transitive groups of degree 48 are not known), and bipartite edgetransitive graphs of order up to 63. It also led us to the answer to a 1967 question by Folkman about the valencytoorder ratio for regular graphs that are edge but not vertextransitive.
Then I'll describe some recent work on edgetransitive maps, helped along by workshops at Oaxaca and Banff in 2017. I'll explain how such maps fall into 14 natural classes (two of which are the classes of regular and chiral maps), and how graphs in each class may be constructed and analysed. This will include the answers to some 18yearold questions by Širáň,
Tucker and Watkins about the existence of particular kinds of such maps on orientable and nonorientable surfaces.
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 "I WISH I'D KNOWN..." SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: How to choose thesis and postdoc project topics
 Location: Room V111, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Nov 2016
 The first in a new series of CARMA seminars.
 Abstract:
Targeted Audience: All early career staff and PhD students; other staff welcome
Abstract: Many of us have been involved in discussions revolving around the problem of choosing suitable thesis topics and projects for postgraduate students, honours students and vacation research students. The panel is going to present some ideas that we hope people in the audience will find useful as they get ready for or continue with their careers.
About the Speakers: Professor Brian Alspach has supervised thirteen PhDs, twentyfive MScs, nine postdoctoral fellows and a dozen undergraduate scholars over his fiftyyear career. Professor Eric Beh has 20 years' international experience in the analysis of categorical data with a focus on data visualisation. He has and has, or currently is, supervised about a 10 PhD students. Dr Mike Meylan has twenty years research experience in applied mathematics both leading projects and working with others. He has supervised 5 PhD students and three postdoctoral fellows.
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 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: HoffmanSingleton paper of 1964
 Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Mon, 7^{th} Nov 2016
 Abstract:
Today's discrete mathematics seminar is dedicated to Mirka Miller. I am going to present the beautiful HoffmanSingleton (1964) paper which established the possible values for valencies for Moore graphs of diameter 2, gave us the HoffmanSingleton graph of order 50, and gave us one of the intriguing still unsettled problems in combinatorics. The proof is completely linear algebra and is a proof that any serious student in discrete mathematics should see sometime. This is the general area in which Mirka made many contributions.
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 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: Orthogonalizeable groups
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Wed, 6^{th} Apr 2016
 Abstract:
B. Gordon (1961) defined sequenceable groups and G. Ringel (1974) defined Rsequenceable groups. Friedlander, Gordon and Miller conjectured that finite abelian groups are either sequenceable or Rsequenceable. The preceding definitions are special cases of what T. Kalinowski and I are calling an orthogonalizeable group, namely, a group for which every Cayley digraph on the group admits either an orthogonal directed path or an orthogonal directed cycle. I shall go over the history and current status of this topic along with a discussion about the completion of a proof of the FGM conjecture.
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 AUSTRALIAN MATHEMATICAL SCIENCES STUDENT CONFERENCE
 Public Lecture
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: Lost Spelunkers, Cops And Robbers and Is Someone Trying To Destroy My Network?
 Location: Room V07, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 6:30 pm, Wed, 2^{nd} Jul 2014
 Abstract:
What do the three elements of the title have in common is the utility of using graph
searching as a model. In this talk I shall discuss the relatively brief history of graph searching,
several models currently being employed, several significant results, unsolved conjectures, and
the vast expanse of unexplored territory.
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 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The Oberwolfach Problem ReVisited
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 15^{th} May 2014
 Abstract:
This year is the fiftieth anniversary of Ringel's posing of the wellknown graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be selfcontained.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The Oberwolfach Problem ReVisited
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 8^{th} May 2014
 Abstract:
This year is the fiftieth anniversary of Ringel's posing of the wellknown graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be selfcontained.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The Oberwolfach Problem ReVisited
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 17^{th} Apr 2014
 Abstract:
This year is the fiftieth anniversary of Ringel's posing of the wellknown graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be selfcontained.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The proof of ManickamMiklosSinghi
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Apr 2014
 Abstract:
: In this final talk of the sequence we will sketch Blinovsky's recent proof of the conjecture: Whenever n is at least 4k, and A is a set of n numbers with sum 0, then there are at least (n1) choose (k1) subsets of size k which have nonnegative sum. The nice aspect of the proof is the combination of hypergraph concepts with convex geometry arguments and a BerryEsseen inequality for approximating the hypergeometric distribution. The not so nice aspect (which will be omitted in the talk) is the amount of very tedious algebraic manipulation that is necessary to verify the required estimates. There are slides for all four MMS talks here.
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 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: From EKR to MMS
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 3^{rd} Apr 2014
 Abstract:
The ErdosKoRado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of kelement subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection?
In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of kelement subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013.
This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: From EKR to MMS
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 20^{th} Mar 2014
 Abstract:
The ErdosKoRado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of kelement subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection?
In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of kelement subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013.
This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: From EKR to MMS
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 13^{th} Mar 2014
 Abstract:
The ErdosKoRado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of kelement subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection?
In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of kelement subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013.
This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture.
 [Permanent link]
 CARMA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The Anatomy of a Famous Conjecture
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Thu, 12^{th} Apr 2012
 Abstract:
In my opinion, the most significant unsolved problem in graph decompositions is the cycle double conjecture. This begins a series of talks on this conjecture in terms of background, relations to other problems and partial results.
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 CARMAGTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR
 Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
 Title: The EdmondsFulkerson matroid partition theorem
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Thu, 5^{th} May 2011
 Abstract:
We meet this Thursday at the usual time when I will show you a nice application of the EdmondsFulkerson matroid partition theorem, namely, I'll prove that Paley graphs have Hamilton decompositions (an unpublished result).
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