Discrete Mathematics

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).

This week Graham Farr is co-organising with Jo Ellis-Monaghan (Universiteit van Amsterdam), Iain Moffatt (Royal Holloway, University of London) and Kerri Morgan (RMIT University) the MATRIX program Workshop on Uniqueness and Discernment in Graph Polynomials. Jo and Iain will be visiting Monash afterwards.

Welcome to Abdul Basit, who is a new post-doctoral researcher in the Monash Discrete Mathematics Research Group, funded under Daniel Horsley’s ARC grant. Basit’s research interests include combinatorial geometry, extremal and probabilistic graph theory, and additive combinatorics.

PhD students in the discrete maths group have recently written the following single-authored papers (in addition to several multi-authored papers):

Jack Allsop, “Cycles of quadratic Latin squares and anti-perfect 1-factorisations”, J. Combin. Des. 31, (2023), 447-475

Marc Distel, “Proper Minor-Closed Classes of Graphs have Assouad-Nagata Dimension 2”, arXiv:2308.10377

Robert Hickingbotham, “Induced subgraphs and path decompositions”, Electronic J. Combinatorics 30:P2.37, 2023.

Robert Hickingbotham, “Odd colourings, conflict-free colourings and strong colouring numbers”. Australasian J. Combinatorics, accepted 2023. arXiv:2203.10402

Congratulations to Rui Zhang for submitting his PhD thesis “The probability of non-existence of small substructures in moderately sparse random objects (via clusters and cumulants)”, supervised by Nick Wormald. Rui is now working as a postdoctoral researcher in Barcelona with Gabor Lugosi.

This week we are hosting Marcin Briański, who is a visiting PhD student from Jagiellonian University in Poland.

Following last week’s MATRIX-IBS Workshop Structural Graph Theory Downunder III, this week we are hosting several visitors: Kevin Hendrey, Rutger Campbell, Pascal Gollin, Sebastian Wiederrecht (all from IBS Korea), James Davies (from Cambridge), and Liana Yepremyan and Bryce Frederickson (both from Emory).

Well it wasn’t quite an Oscar, but Nick Wormald has won an award surely worthy of the red carpet.

It is the Thomas Ranken Lyle Medal, awarded by the Australian Academy of Science in recognition for his outstanding achievements in mathematical research. The citation recognised that Nick is a world leader in his field: he has made major contributions in the areas of random graphs and processes, enumeration of graphs and maps, structural graph theory, theoretical computer science, and network optimisation. See

https://www.science.org.au/supporting-science/awards-and-opportunities/thomas-ranken-lyle-medal

Welcome to Dr Melissa Lee who has joined the School of Mathematics as Lecturer and DECRA Fellow. Melissa’s research interests include finite group theory, representation theory of almost simple groups, finite geometry and combinatorics.