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Symmetry and Groups 23rd May 2015, Birkbeck

Thank you for participating in this conference on Symmetry and Groups. It has been organised by the British Society for the History of Mathematics (BSHM), with support from the Department of Economics, Mathematics and Statistics at Birkbeck College, University of London. This is the first in what we hope will be a regular annual addition to the BSHM calendar. If you are not already a member of the BSHM, we hope you will consider joining. You can pick up an information form at the conference or go to the website www.bshm.ac.uk for more information.

On Arrival

• The conference will be in the main Birkbeck Building (number 1 on the attached map). For journey planning, the postcode is WC1E 7HX. Nearby stations include Euston, Russell Square and Warren Street.

• Registration and all tea/coffee breaks through the day will be in room B04; this is on the basement level near the main lecture room. It will be clearly signposted.

• All lectures will be in room B36, again on the basement level and clearly signposted.

• The full programme with abstract is on page 2.

• Lunch is not provided. There are numerous cafes, restaurants and shops nearby; a few suggestions are given on page 3.

• The organisers are Sarah Hart and Jane Wess, both of whom serve on BSHM Council. Sarah is at Birkbeck so should be able to help with any location-specific issues on the day.

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Programme 9:30 Registration and Coffee (Room B04) 10:00 Sarah Hart: ‘Symmetry: before groups and after groups’. Abstract: We will look at a few examples of how symmetry was studied pre algebra, remark on its cultural importance over time, and then give a brief roadmap of some of the main names that we will encounter through the rest of the day. 10:40 Peter Neumann: ‘Sigola and permutations: there's little symmetry in Galois’. Abstract: This contribution responds to a request for a talk on Galois and/or related topics. As the title indicates, it will involve Evariste Galois, symmetry and permutations. The focus will be more history of mathematics than mathematics itself. 11:30 Tea/Coffee 11:50 Norman Biggs: ‘Coxeter and Conway on the Symmetry of Graphs and Maps’. Abstract: In this talk I shall describe how the idea of symmetry was developed mathematically, particularly in the context of graphs and maps on surfaces. The key is the description of a group by means of generators and relations. H.S.M. Coxeter wrote many seminal papers on this subject, and his colleague W.T. Tutte obtained some remarkable results. In the 1960s this theory was rediscovered in unpublished work by J.H. Conway. He developed an approach that allowed the computational technique known as ‘coset enumeration’ to be applied, and this resulted in some beautiful examples of highly symmetric graphs. 12:40 Lunch 14:00 Mark Ronan: ‘Les belles au bois dormant: Strange beauties hidden in the undergrowth’. Abstract: This talk will discuss the discovery of the sporadic groups during the 1960s and 70s. 14:50 Rob Curtis: ‘Sphere-packing, the Leech lattice and the Conway group’. Abstract: What proportion of n-dimensional space can be filled by non-overlapping n-spheres all of the same size? This natural and innocent-sounding question is remarkably difficult to answer, even in low dimensions. However, if we restrict our attention to highly symmetrical arrangements of spheres known as lattice packings the problem becomes more tractable. In general there is no guarantee that lattice packings are optimal; but it turns out that in both 8 and 24 dimensions there are beautifully symmetrical arrangements of spheres based on the E8 and Leech lattices which have been proven to be best possible. Both structures have large groups of symmetries, and in the latter case it is the Conway group ⋅O. In this talk we explore sphere-packing in low dimensions, then briefly describe the E8 lattice before moving on to 24 dimensions. We conclude by showing how ⋅O can be obtained directly by considering a group with certain internal symmetries. The Leech lattice then emerges as a by-product. 15:40 Tea/Coffee 16:00 Siobhan Roberts: ‘Symmetries & Asymmetries, Coxeter & Conway’. Abstract: Wherein the author “measures together” the mutual obsession with symmetry possessed by H.S.M. Coxeter and John Horton Conway, drawing from her experience in writing their respective biographies, King of Infinite Space (2006) and Genius At Play (2015). 17:00 End

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Places to Eat near Birkbeck

• We have an hour and twenty minutes for lunch.

• Within Birkbeck, on the ground floor by the foyer, we have a Costa Coffee open from 9am which has a range of sandwiches, hot paninis and snacks.

• The Birkbeck Student Union Shop (Room B28) is located in the basement of the main building, below the foyer, and is open from 11am – 5pm on Saturdays. It sells hot beverages, sandwiches, wraps, bagels, confectionary and snacks.

• Externally there are several shops where you can buy sandwiches and snacks - you can bring these back and have them in room B04 if you wish. The nearest are the Paradise Deli and the Co-op Local on Store Street, (South-West of Birkbeck on the map) or the Pret-a-Manger and Tesco Metro opposite Russell Square Tube. Store Street and Russell Square are marked on the map.

• The Marlborough Arms (36 Torrington Place – turn left out of Birkbeck, then left again, passing Waterstones on your left –Waterstones is marked on the map) is the nearest pub, it serves standard pub food.

• Planet Organic on Torrington Place (left out of Birkbeck then left again, passing Waterstones and the Marlborough Arms on your left, and crossing Gower Street) sells vegetarian and vegan food to eat in or take away.

• Olivelli’s on Store Street has a cheapish set lunch.

• The Russell Square Café in Russell Square is also reasonable and close at hand.