- SYMMETRY IN NEWCASTLE
- Location: Room V109, Mathematics Building (Callaghan Campus) The University of Newcastle
- Dates: Fri, 2nd Aug 2019 - Fri, 2nd Aug 2019
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Schedule:
12-1: Brian Alspach
1-2: Lunch
2-3: John Bamberg
3-3.30: Tea
3.30-4.30: 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 (1973-1974) (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: Edge-transitive graphs and maps
- Abstract for Edge-transitive graphs and maps:
In this talk I'll describe some recent discoveries about edge-transitive graphs and edge-transitive maps. These are objects that have received relatively little attention compared with their vertex-transitive and arc-transitive siblings.
First I will explain a new approach (taken in joint work with Gabriel Verret) to finding all edge-transitive graphs of small order, using single and double actions of transitive permutation groups. This has resulted in the determination of all edge-transitive graphs of order up to 47 (the best possible just now, because the transitive groups of degree 48 are not known), and bipartite edge-transitive graphs of order up to 63. It also led us to the answer to a 1967 question by Folkman about the valency-to-order ratio for regular graphs that are edge- but not vertex-transitive.
Then I'll describe some recent work on edge-transitive 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 18-year-old questions by Širáň,
Tucker and Watkins about the existence of particular kinds of such maps on orientable and non-orientable 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 (1973-1974) (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 Edge-transitive graphs and maps:
In this talk I'll describe some recent discoveries about edge-transitive graphs and edge-transitive maps. These are objects that have received relatively little attention compared with their vertex-transitive and arc-transitive siblings.
First I will explain a new approach (taken in joint work with Gabriel Verret) to finding all edge-transitive graphs of small order, using single and double actions of transitive permutation groups. This has resulted in the determination of all edge-transitive graphs of order up to 47 (the best possible just now, because the transitive groups of degree 48 are not known), and bipartite edge-transitive graphs of order up to 63. It also led us to the answer to a 1967 question by Folkman about the valency-to-order ratio for regular graphs that are edge- but not vertex-transitive.
Then I'll describe some recent work on edge-transitive 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 18-year-old questions by Širáň,
Tucker and Watkins about the existence of particular kinds of such maps on orientable and non-orientable 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 post-doc project topics
- Location: Room V111, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Thu, 10th 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 post-graduate 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, twenty-five MScs, nine post-doctoral fellows and a dozen undergraduate scholars over his fifty-year 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 post-doctoral fellows.
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- CARMA DISCRETE MATHEMATICS SEMINAR
- Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
- Title: Hoffman-Singleton paper of 1964
- Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 3:00 pm, Mon, 7th Nov 2016
- Abstract:
Today's discrete mathematics seminar is dedicated to Mirka Miller. I am going to present the beautiful Hoffman-Singleton (1964) paper which established the possible values for valencies for Moore graphs of diameter 2, gave us the Hoffman-Singleton 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, 6th Apr 2016
- Abstract:
B. Gordon (1961) defined sequenceable groups and G. Ringel (1974) defined R-sequenceable groups. Friedlander, Gordon and Miller conjectured that finite abelian groups are either sequenceable or R-sequenceable. 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, 2nd 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 Re-Visited
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Thu, 15th May 2014
- Abstract:
This year is the fiftieth anniversary of Ringel's posing of the well-known 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 self-contained.
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- CARMA DISCRETE MATHEMATICS SEMINAR
- Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
- Title: The Oberwolfach Problem Re-Visited
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Thu, 8th May 2014
- Abstract:
This year is the fiftieth anniversary of Ringel's posing of the well-known 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 self-contained.
- [Permanent link]
- CARMA DISCRETE MATHEMATICS SEMINAR
- Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
- Title: The Oberwolfach Problem Re-Visited
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Thu, 17th Apr 2014
- Abstract:
This year is the fiftieth anniversary of Ringel's posing of the well-known 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 self-contained.
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- CARMA DISCRETE MATHEMATICS SEMINAR
- Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
- Title: The proof of Manickam-Miklos-Singhi
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 4:00 pm, Thu, 10th 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 (n-1) choose (k-1) subsets of size k which have non-negative sum. The nice aspect of the proof is the combination of hypergraph concepts with convex geometry arguments and a Berry-Esseen 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, 3rd Apr 2014
- Abstract:
The Erdos-Ko-Rado (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 k-element 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 k-element 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.
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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, 20th Mar 2014
- Abstract:
The Erdos-Ko-Rado (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 k-element 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 k-element 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, 13th Mar 2014
- Abstract:
The Erdos-Ko-Rado (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 k-element 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 k-element 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.
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- 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, 12th 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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- CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR
- Speaker: Prof. Brian Alspach, CARMA, The University of Newcastle
- Title: The Edmonds-Fulkerson matroid partition theorem
- Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 3:00 pm, Thu, 5th May 2011
- Abstract:
We meet this Thursday at the usual time when I will show you a nice application of the Edmonds-Fulkerson matroid partition theorem, namely, I'll prove that Paley graphs have Hamilton decompositions (an unpublished result).
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