Department of Mathematics and Statistics
University of Melbourne
Parkville, Victoria 3010
Email m.payne3 "arroba" pgrad.unimelb.edu.au
- I recently finished my PhD under the supervision of David
Wood, who is now at Monash University.
- My research interests centre around discrete geometry and geometric graph theory.
- Together with Helmut Alt and Jens Schmidt from Theoretical Computer Science at FU Berlin, David Wood and I were awarded a Go8/DAAD Joint Research Co-Operation Scheme
grant for 2011/2012.
- I did 'Phase I' at the Berlin Mathematical School. There I was a member of Günter M. Ziegler's Discrete Geometry group at TU Berlin (since relocated to FU Berlin).
- I did my undergraduate studies in Australia at Monash University.
- I have attended various conferences and workshops:
MDS Workshop: Order and Geometry (TU Berlin),
MDS Summer School: Order and Geometry (Döllnsee),
MCW19 (Charles University),
AMSI Workshop: Mathematics of Transport Networks (Monash),
AMSI Workshop: Optimisation in Industry (RMIT),
MCW18 (Charles University),
EGC2011 (Alcalá de Henares),
Geometric Graph Theory (EPFL),
Bernoulli Conference on DCG (EPFL),
- Empty pentagons in point sets with collinearities, with János Barát, Vida Dujmović, Gwenaël Joret, Ludmila Scharf, Daria Schymura, Pavel Valtr and David R. Wood, to appear in SIAM J. Discrete Math.
- Progress on Dirac's conjecture, with David R. Wood, Electron. J. Combin. 21 (2014), no. 2, Paper 12.
- Which point sets admit a k-angulation?, with Jens M. Schmidt and David R. Wood, J. Comput. Geom. 5 (2014), no. 1.
- On the general position subset selection problem, with David R. Wood, SIAM J. Discrete Math. 27 (2013), no. 4, 1727-1733.
- On the connectivity of visibility graphs, with Attila Pór, Pavel Valtr and David R. Wood, Discrete Comput. Geom. 48 (2012), no. 3, 669-681.
- Unit distance graphs with ambiguous chromatic number, Electron. J. Combin. 16 (2009), no. 1, Note 31.
- A dense distance 1 excluding set in R3, with D. Coulson, Austral. Math. Soc. Gaz. 34 (2007), no. 2,
Here is my PhD Thesis. Here are some lp_solve files related to my work on a conjecture of Kleitman and Pinchasi (see Chapter 6). See the included readme.txt for how to interpret them.