Benjamin Burton

Regina: Software for 3-manifold topology and normal surface theory
About me
Research, publications and grants
PhD and honours supervision
Teaching at UQ
Informatics and mathematics olympiads
Software
Contact details

Last updated: 22 January 2015

About me

Me I am a mathematician who enjoys working with ideas from computer science. My main interest is in computational geometry and topology, which basically means I get to play with geometry on supercomputers. One of my larger projects is working on the topological software Regina.

I am currently Associate Professor in the School of Mathematics and Physics at the University of Queensland, Brisbane, Australia, where I have just finished a QEII Fellowship. I have previously worked in the mathematics departments at RMIT University, the University of Melbourne and Oklahoma State University, as well as a three-year stint in the finance industry.

I am a great fan of enrichment programmes for high school students, and I have a long involvement with the Informatics Olympiad, the Mathematics Olympiad and the National Mathematics Summer School. See below for details.

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Research, publications and grants

Trivial and non-trivial loops on surfaces My main research area is computational geometry and topology, with a focus on spaces in three and four dimensions. I am particularly interested in developing practical software in this setting, and in understanding the intrinsic difficulty of fundamental problems in this field. I draw on techniques from a variety of areas, including pure mathematics, computer science, combinatorics and operations research.

Other research interests include algorithm design, computational complexity, cryptography, combinatorics, and the development of programming competitions.

You can browse my publications and talks, as well as the research grants that fund my various projects. Much of my work on computational geometry and topology is available through the open-source software package Regina.

We run a weekly informal computational geometry & topology / discrete algorithms meeting, where staff and/or students talk for an hour about their research, or a paper, or just something that others might like to learn about. See the schedule of speakers, and of course feel free to come along if something tickles your fancy.

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PhD and honours supervision

If you are interested in talking about honours projects, summer research projects or possible areas for a PhD, send me an email and I'll be happy to meet up for a chat.

Research topics would draw on the fields of geometry, topology, combinatorics, algorithmics and/or operations research, and would typically involve the interplay between several of these areas. Some examples:

This list is by no means exhaustive, and you are of course welcome to bring along your own ideas.

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Teaching at UQ

My contact hours are Monday 4–5 and Thursday 2–3.

Discrete Mathematics (MATH 1061)

I am teaching and coordinating this course in Semester 1, 2015. Stay tuned for more information.

Coding and Cryptography (MATH 3302)

I am coordinating this course and teaching the cryptography half in Semester 1, 2015. Again, stay tuned for more information.

Past courses at UQ

Semester 2, 2013: MATH 3500 (two-week module on game theory)
Semester 2, 2012: MATH 3500 (two-week module on game theory)
Semester 2, 2011: MATH 3500 (two-week module on game theory)
Semester 1, 2011: MATH 3302 (half-semester on cryptography)
Semester 2, 2010: MATH 3500 (two-week module on game theory)
Semester 2, 2009: MATH 1052 (half-semester on differential equations)

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Informatics and mathematics olympiads

IOI logo The International Olympiad in Informatics (IOI) is the premier competition worldwide for high school students in computer programming and algorithm design, with teams from 80–90 countries competing each year.

I have been involved in the Australian programme since its inception in 1998, acting as Director of Training (1999–2008), Team Leader (2001–2008) and Deputy Leader (1999–2000). I am currently a member of the International Committee (2015–2017), which oversees the Olympiad as a whole, and I have just finished a six-year term on the International Scientific Committee (2009–2014), which oversees the scientific content and development of the IOI.

We have recently kicked off the Queensland Informatics & Programming club (QIP), a Brisbane-based forerunner to the national Informatics Olympiad programme. This is a great place for interested high school students to meet like-minded people, do some programming and learn about algorithms. See the QIP site for details!

Some big news from last year: IOI 2013 was held in Australia! The event was hosted at the University of Queensland in partnership with the Australian Mathematics Trust, and by now many of the organisers may have even recovered. We hope you all had fun!

Before my time with the IOI, I was involved with the Australian Mathematical Olympiad Programme. I also continue to teach courses in surfaces and knot theory at the National Mathematics Summer School.

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Software

Regina logo I am a great believer in open-source software, and I have spent much time working with open-source projects over the years. Some projects I am currently involved in:

If you are looking for specific software related to a paper of mine, try my code page.

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Contact details

Phone, email and locationPostal address
+61-7-3365 1164
bab at maths.uq.edu.au
Building 67, room 547
School of Mathematics and Physics
The University of Queensland
Brisbane QLD 4072, Australia

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