Welcome! The CMSA seminar aims to bring together combinatorialists of Australasia and the world. It is started during the COVID-19 lockdown days, and may continue afterwards. We plan to hold the seminar roughly every two weeks on Wednesday, starting on the 20th of May.

Videos of some past talks can be found here.

Subscribe: Email cmsa-webinar AT monash.edu with the subject "subscribe". We send announcements and zoom details before every talk.

Organisers: Anita Liebenau and Nina Kamčev. Please email us with your feedback and suggestions.

We will mainly be using one of the following two time slots, conversion to your time zone is available via the links:
11am AEST, 9pm ET or 5pm AEST, 9am CET .

Date (AEST)SpeakerTitle Video
20 May '20, 11am Brendan McKay A scientist's adventure into pseudoscience: the strange case of the Bible Codes
3 Jun '20, 4pm John Bamberg Vanishing Krein Parameters in Finite Geometry Video
17 Jun '20, 5pm Fiona Skerman Branching processes with merges and locality of hypercube's critical percolation
1 Jul '20, 5pm Tibor Szabó Turán numbers, norm graphs, quasirandomness
15 Jul '20, 11am Daniel Horsley Generating digraphs with derangements Video
22 Jul '20, 5pm Katherine Staden Two conjectures of Ringel Video
29 Jul '20, 5pm Annika Heckel Non-concentration of the chromatic number Video Slides
19 Aug '20, 11am Tamás Makai Majority dynamics in the dense binomial random graph
26 Aug '20, 11am Tuan Tran tbc
9 Sep '20, 11am Geertrui Van de Voorde tbc

19 August 2020, 11am AEST Tamás Makai (UNSW Sydney)
Majority dynamics in the dense binomial random graph
Abstract: Majority dynamics is a deterministic process on a graph which evolves in the following manner. Initially every vertex is coloured either red or blue. In each step of the process every vertex adopts the colour of the majority of its neighbours, or retains its colour if no majority exists.
We analyse the behaviour of this process in the dense binomial random graph when the initial colour of every vertex is chosen independently and uniformly at random. We show that with high probability the process reaches complete unanimity, partially proving a conjecture of Benjamini, Chan, O'Donnel, Tamuz and Tan.
This is joint work with N. Fountoulakis and M. Kang.

29 July 2020, 5pm AEST Annika Heckel (LMU Munich)
Non-concentration of the chromatic number
Abstract: There are many impressive results asserting that the chromatic number of a random graph is sharply concentrated. In 1987, Shamir and Spencer showed that for any function p=p(n), the chromatic number of G(n,p) takes one of at most about n1/2 consecutive values whp. For sparse random graphs, much sharper concentration is known to hold: Alon and Krivelevich proved two point concentration whenever p < n-1/2-ε.
However, until recently no non-trivial lower bounds for the concentration were known for any p, even though the question was raised prominently by Erdős in 1992 and Bollobás in 2004.
In this talk, we show that the chromatic number of G(n,1/2) is not whp contained in any sequence of intervals of length n1/2-o(1), almost matching Shamir and Spencer's upper bound.
Joint work with Oliver Riordan.

22 Jul 2020, 5pm AEST Katherine Staden (University of Oxford)
Two conjectures of Ringel
Abstract: In a graph decomposition problem, the goal is to partition the edge set of a host graph into a given set of pieces. I will focus on the setting where the host graph and the pieces have a comparable number of vertices, and in particular on two conjectures of Ringel from the 60s on decomposing the complete graph: in the first (Ringel's conjecture) they are identical half-sized trees, and in the second (the Oberwolfach problem) they are identical 2-factors. I will give some ideas from my recent proofs of the first problem and a generalised version of the second, for large graphs, in joint work with Peter Keevash. The first conjecture was proved independently by Montgomery, Pokrovskiy and Sudakov.

15 Jul 2020, 11am AEST Daniel Horsley (Monash University)
Generating digraphs with derangements
Abstract: Let S be a collection of derangements (fixed point-free permutations) of a possibly infinite set X. The derangement action digraph DA(X,S) is the digraph on vertex set X that has an arc from x to y if and only if some derangement in S maps x to y. We say that S generates DA(X,S). Derangement action digraphs were introduced by Iradmusa and Praeger in 2019, adapting the definition of a group action digraph due to Annexstein, Baumslag and Rosenberg.
I will discuss recent work by Iradmusa, Praeger and myself in which we characterise, for each positive integer k, the digraphs that can be generated by at most k derangements. Our result resembles the De Bruijn-Erdős theorem in that it characterises a property of an infinite graph in terms of properties of its finite subgraphs.

1 Jul 2020, 5pm AEST Tibor Szabó (Freie Universität Berlin)
Turán numbers, norm graphs, quasirandomness
Abstract: The Turán number of a (hyper)graph H, defined as the maximum number of (hyper)edges in an H-free (hyper)graph on a given number of vertices, is a fundamental concept of extremal combinatorics. The behaviour of the Turán number is well-understood for non-bipartite graphs, but for bipartite H there are more questions than answers. A particularly intriguing half-open case is the one of complete bipartite graphs.
The projective norm graphs NG(q,t) are algebraically defined graphs which provide tight constructions in the Turán problem for complete bipartite graphs H=Kt,s when s>(t–1)!. The Kt,s-freeness of NG(q,t) is a very much atypical property: in a random graph with the same edge density a positive fraction of t-tuples are involved in a copy of Kt,s. Yet, projective norm graphs are random-like in various other senses. Most notably their second eigenvalue is of the order of the square root of the degree, which, through the Expander Mixing Lemma, implies further quasirandom properties concerning the density of small enough subgraphs. In this talk we explore how far this quasirandomness goes. The main contribution of our proof is the estimation, and sometimes determination, of the number of solutions of certain norm equation system over finite fields.
Joint work with Tomas Bayer, Tamás Mészáros, and Lajos Rónyai.

17 Jun 2020, 5pm AEST Fiona Skerman (Uppsala University)
Branching processes with merges and locality of hypercube's critical percolation
Abstract: We define a branching process to understand the locality or otherwise of the critical percolation in the hypercube; that is, whether the local structure of the hypercube can explain the critical percolation as a function of the dimension of the hypercube.
The branching process mimics the local behaviour of an exploration of a percolated hypercube; it is defined recursively as follows. Start with a single individual in generation 0. On an first stage, each individual has independent Poisson offspring with mean (1+p)(1-q)k where k depends on the ancestry of the individual; on the merger stage, each pair of cousins merges with probability q.
We exhibit evidence of a critical merger probability qc=qc(p) for extinction of the branching process. When p is sufficiently small, the first order terms of qc coincide with those of the critical percolation for the hypercube, suggesting that percolation in the hypercube is dictated by its local structure. This is work in progress with Laura Eslava and Sarah Penington.

3 Jun 2020, 4pm AEST John Bamberg (University of Western Australia)
Vanishing Krein Parameters in Finite Geometry
Abstract: The Krein condition on the parameters of a strongly regular graph (L. L. Scott 1973, 1977) is one of the most successful tools in ruling out sets of possible parameters of strongly regular graphs. Delsarte’s generalisation for association schemes (1973) has also played an important role in the theory of association schemes and its applications: to coding theory, design theory, and finite geometry. In this talk, we give a brief introduction to the interplay between association schemes and finite geometry, and some recent results on vanishing Krein parameters of the speaker and his student Jesse Lansdown.

20 May 2020, 11am AEST Brendan McKay (Australian National University)
A scientist's adventure into pseudoscience: the strange case of the Bible Codes
Abstract: Over the centuries, many claims have been made of numerical patterns of miraculous nature hidden within the text of sacred writings, including the Jewish, Christian and Islamic scriptures. Usually the patterns involve counting of letters and words, or calculations involving numerical equivalents of the letters.
Until recently, all such claims were made by people with little mathematical understanding and were easily explained. This situation changed when a highly respected Israeli mathematician Eliyahu Rips and two others published a paper in the academic journal Statistical Science claiming to prove that information about medieval Jewish rabbis was encoded in the Hebrew text of the Book of Genesis. The journal reported that its reviewers were "baffled".
The paper in Statistical Science spawned a huge "Bible Codes" industry, complete with best selling books, TV documentaries, and even an adventure movie.
The talk will reveal the inside story of the Codes and the people behind them, from their inception through to their refutation.