Discrete Mathematics

Welcome to André Kündgen, who is visiting the group on sabbatical from California State University San Marcos.

We’re very excited to be advertising 5 permanent jobs at Monash. The positions can be in any area of mathematics, but discrete maths (including graph theory and combinatorics) is designated as a priority area. For the formal details see:

https://careers.pageuppeople.com/513/cw/en/job/660206/expressions-of-interest-multiple-positions-as-lecturer-senior-lecturer-associate-professor

Please spread the word and/or apply yourself. We can appoint young or established researchers, singles or couples. Monash discrete maths group is internationally important and Melbourne regularly features highly in lists of the world’s most liveable cities. So come and join us!

For any enquiries, email ian.wanless@monash.edu

Congratulations to Nina Kamčev for winning the inaugural CMSA Prize for her work completed at Monash University that led to the following papers:

N. Kamčev, A. Liebenau and N. Morrison, Towards a characterisation of Sidorenko systems, The Quarterly Journal of Mathematics.

N. Kamčev, A. Liebenau and N. Morrison, On uncommon systems of equations, Israel Journal of Mathematics.

The prize was announced today at the 45th ACC in Perth, where Nina gave an invited talk on her work.

This week, several group members are attending the MATRIX workshop Extremal Problems in Graphs, Designs, and Geometries organised by Daniel Horsley, Anita Liebenau (UNSW) and Tibor Szabo (Freie Universitat Berlin).

Visitors this week include Padraig Ó Catháin from Dublin City University and Tibor Szabó from Freie Universität Berlin.

This week Heiko, Santiago, Tomasz and Melissa are co-organisers of the 7th Australian Algebra Conference, held at Monash.

Some recent papers by group members:

Anita Liebenau, Nick Wormald
Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph
J. European Math. Society 2023

Vida Dujmović, Louis Esperet, Pat Morin, David R. Wood.
Proof of the clustered Hadwiger conjecture
Proc. 64th IEEE Symposium on Foundations of Computer Science (FOCS ’23)

Aidan R. Gentle, Ian M. Wanless
On perfect sequence covering arrays
Annals Comb. 2023

Alexander Cant, Heiko Dietrich, Bettina Eick, and Tobias Moede.
Galois trees in the graph of p-groups of maximal class.
J. Algebra 2022.

Anita Liebenau, Nick Wormald
Asymptotic enumeration of digraphs and bipartite graphs by degree sequence
Random Structures Algorithms 2023

Vida Dujmović, Pat Morin, David R. Wood.
Graph product structure for non-minor-closed classes
J. Combinatorial Theory Series B 2023

Catherine Greenhill, Mikhail Isaev, Tamás Makai, Brendan D. McKay
Degree sequences of sufficiently dense random uniform hypergraphs
Combin. Probab. Comput. 2023

David Eppstein, Robert Hickingbotham, Sergey Norin, Laura Merker, Michal T. Seweryn, David R. Wood.
Three-dimensional graph products with unbounded stack-number
Discrete & Computational Geometry 2023

Ajani De Vas Gunasekara, Daniel Horsley
An Evans-style result for block designs
SIAM J. Discrete Math. 2022

Timothy C. Burness, Melissa Lee
On the classification of extremely primitive affine groups
Israel J. Math. 2023

Antonio Girão, Freddie Illingworth, Alex Scott, David R. Wood.
Defective colouring of hypergraphs
Random Structures Algorithms, 2023

The group once again featured in the Research Magazine of The Australian newspaper today.

Discrete Mathematics
Lead institution: Monash
Field leader: David Wood

Theoretical Computer Science
Lead institution: Monash
Field leader: Nick Wormald

Pure & Applied Mathematics
Lead institution: Monash
Field leader: David Wood

This week, Gabriel Verret from the University of Auckland is visiting Melissa Lee.

Group members were successful in today’s announcement of ARC Discovery Projects:

Fractional decomposition of graphs and the Nash-Williams conjecture. Daniel Horsley, Darryn Bryant (U. Queensland), Barbara Maenhaut (U. Queensland), Peter Dukes (U. Vic.).

The Global Structure of Sparse Networks. David Wood, Vida Dujmović (U. Ottawa).