This meeting is intended as an introduction to the Society's Annual General Meeting later in the day, All graduate students (and indeed any other mathematicians) are very welcome.

09.30               Registration – Goodenough College (Tea and coffee available)

10.00               Professor Viveka Erlandsson (Bristol) – Hyperbolic surfaces and counting curves: Part 1

10.45               Tea/Coffee Break (until 11.00)

11.00               Professor Viveka Erlandsson (Bristol) – Hyperbolic surfaces and counting curves: Part 2

11.45               Graduate Student Talks

11.45   Ruoyi Wang          When shifted primes do not occur in difference sets

12.00   Leyu Han             Centre of centralizer of nilpotent element in Lie superalgebras

12.15               Lunch (until 12.45)

12.45   André Macedo        Local-to-global principles for solving Diophantine equations 

13.00   Jared Duker Lichtman   Erdos' primitive set conjecture 

13.15   Carl-Fredrik Nyberg Brodda   Special Semigroups and Monadic Monoids

13.30               Professor David Singerman (Southampton) - Bob Riley and some applications of discrete groups.

14.00               Prize award and Graduate Student Meeting ends

The Society's Annual General Meeting, a Society meeting open to all, will follow the Graduate Student Meeting, from 2.30pm to 6.00pm.

Speakers

Professor Marc Lackenby (Oxford)

Title: The complexity of knots

Abstract: In his final paper in 1954, Alan Turing said 'No systematic method is yet known by which one can tell whether two knots are the same.' Wolfgang Haken and Geoffrey Hemion discovered such a method over 20 years later. However, the computational complexity of this problem remains unknown. In other words, we do not know just how complicated knots are. In my talk, I will give a survey of some of the recent results in this area. Along the way, we will meet some hyperbolic geometry , the 'P ≠ NP' conjecture, and some very very big numbers.

Professor Caroline Series FRS (Warwick)

Presidental Address

Title: All About the Riley Slice

Abstract: The Riley slice is the name given to the family of subgroups of   generated by two parabolic Möbius maps  and . Here c ≠0 is a parameter which rangers over the complex plane. Thanks to work of many people over many years, we now have very detailed understanding of this entire parameter space. It include groups which are free and discrete, but also many non-discrete groups. Among non-free discrete groups it includes all those which give rise to a hyperbolic structure on the complement of a two bridge knot. It also illustrates many of the major results of Thurston and his school. We will give a tour of the parameter space and the geometry of the groups in it, taking as our starting point the remarkable computer explorations made by Robert Riley in Southampton in the 1970s, and comparing it to the picture discovered by myself and Linda Keen which shows the set of all free discrete groups foliated by rays which have a natural geometric interpretation.

Place are free and all refreshments including lunch will be provided.

Travel grants of up to £50 are available to students who attend both the Graduate Student Meeting the Society's General Meeting.

The General Meeting will be followed by a reception and the LMS Annual Dinner at Goodenough College at 7.30 pm.