## Previous Events

Unless otherwise stated, the talks were held at 7pm in MR2 at the Centre for Mathematical Sciences (the CMS), Wilberforce Road.

To view current and upcoming events, please visit the Events page.

## Easter 2016

 29th April, Solving equations with topology, Dr. Oscar Randall-Williams Topology is often useful in showing that equations have solutions without necessarily finding out what the solutions are. The first example of this is the intermediate value theorem: a continuous function f: R → R which takes both positive and negative values must take the value 0; the topological input is that R is connected. The second of these is the fundamental theorem of algebra: a polynomial function p: C → C of positive degree must take the value 0; the topological input is the calculation of the fundamental group of the circle. I will explain these as well as the less-well known example of solving equations in groups: given a "polynomial" such as w(x)=g1 x2 g2 x-4 g3 x3 with g1, g2, g3 in a group G and x a formal symbol, is there a bigger group H ≥ G and a h ϵ H such that w(h)=e ϵ H? 1st May, 6:30pm, Pizza and Board Games Night, Pavillion D Common Room 16th May, Projective Planes and the Magic Square, Professor Michael Atiyah Few things are more important and more fun than complex numbers and their generalizations: quaternions and octonians. There is a magic about them that has fascinated mathematicians over the centuries. I will tell this story from its origins in the 18th and 19th centuries and bring it right up to to the present time, on the front line of current research.

## Lent 2016

 29th January, Bayesian inference and the Bernstein-von Mises theorem, Dr Richard Nickl (Statslab) Many statisticians believe there is a fundamental division between two 'religious' paradigms, known in scientific folklore as the 'Bayesians' and the 'frequentists'. The former have some 'subjective beliefs' modelled through a prior distribution that then is 'updated' given new observations (via a triviality known as 'Bayes' theorem'). In contrast the frequentists let their inferences be dictated by the empirical evidence of the data alone, and accuse the Bayesian approach of lack of scientific rigour. In this talk I will discuss the history of a beautiful theorem from mathematical statistics that reconciles these two paradigms from a frequentist point of view: The Bernstein-von Mises phenomenon, which was first discovered by Laplace in a simple case and worked out as a general theorem by mathematicians in the 20th century, states that Bayesian inference based on the posterior distribution is actually 'in most cases frequentist optimal', in a sense I will explain. If time permits I will also touch on some recently discovered mathematical surprises in 'high-dimensional' versions of the Bernstein von Mises theorem, as is relevant in statistical methodology used in the recent 'data science hype' involving buzzwords such as 'big data', 'machine learning' and 'Bayesian nonparametrics'. 5th February, 7:30pm, An Old Problem, Professor Béla Bollobás (DPMMS) Most mathematical problems are solved a few years after they are posed, but some (not only Fermat's Last Theorem) take over a century to solve. In this talk I shall present a simple solution of a problem posed over a century ago. 12th February, Universality in probability theory, Professor Martin Hairer (Warwick) Some objects in probability theory are "universal", i.e. they arise naturally in many different, only loosely related, contexts. We will discuss some of these objects and try to give a glimpse of some of the progress made over the past years towards their understanding. 19th February, Galois and his groups, Peter Neumann (Oxford) When Galois invented groups they were very different from the structures taught and learned and loved in undergraduate courses at Cambridge and other modern universities. My purpose in this lecture will be to explain the differences and calibrate the similarities. As a by-product I hope to show that topics in the History of Mathematics can be just as exciting, subtle and difficult as mathematics itself. 20th February, 7:00pm, Archimedeans Annual Dinner, Doubletree by Hilton Hotel 25th February, Molecular Dynamics, Random Walks and PDEs, Radek Erban (Oxford) I will introduce several deterministic and stochastic dynamical systems which have been used for mathematical modelling in biology, describing processes at different spatial and temporal scales. Using simple illustrative examples, I will discuss connections between (detailed) molecular dynamics simulations, (less detailed) Brownian dynamics approaches and (even coarser) models written as partial differential equations. I will use this discussion to highlight some open mathematical problems in the field of mathematical biology.Note: This talk is on a Thursday, rather than a Friday, but will still be at 7pm. 11th March, Combinatorics and the Fourier Transform, Tom Sanders (Oxford)

## Michaelmas 2016

 7th October, High Dimensions, Prof. Imre Leader (DPMMS) It is hard enough to visualise complicated shapes in three dimensions, or indeed to visualise any shapes in four dimensions. What happens when the number of dimensions is much larger? In this talk, we will investigate some of the phenomena of "high dimensions". 13th October (Thursday), 8:00pm, Our Universe and Others (Maxwell Lecture), Lord Martin Rees (IoA) The illustrated talk will describe some recent discoveries about planets (around other stars as well as in our Solar System), black holes, galaxies and the big bang.It will also speculate about whether ‘our’ big bang was the only one. 20th October (Thursday), 7:00pm, Pub Quiz Come and see which team has the least bad popular culture knowledge! Not really. Most questions will be in some way maths-related, but a couple of rounds will be more in the style of a typical pub quiz question. Good fun and with a mystery prize up for grabs, the pub quiz is an event not to be missed. 11th November, Number theory and dynamics: a how-to guide, Dr. Holly Krieger (DPMMS) Diophantine problems in number theory are among some of the easiest to state, and the most difficult to prove. However, spectacular progress has been made on some of these problems by translating them to the theory of dynamical systems. I will explain some of these connections, including the Oppenheim conjecture, Littlewood's conjecture, and the arithmetic of elliptic curves. 18th November, Quantum Simulators with Polariton Graphs, Prof. Natalia Berloff (DAMTP) Several platforms were recently proposed for addressing problems whose complexity increases faster than polynomially with the number of variables or degrees of freedom in the system. Many of these computationally intractable problems can be mapped into universal classical spin models such as the Ising and the XY models and simulated by a suitable physical system. I will talk about our recent theoretical and experimental effort in using a new hybrid light-matter particle, exciton-polariton, and polariton graphs as an effient simulator for finding the global minimum of the classical XY Hamiltonian. 25th November, Mathematical Thinking: Fast and Slow, Prof. Martin Hyland (DPMMS) It is generally agreed that the aim of a mathematics education should be at least inter alia to develop mathematical thinking. However people have very different ideas as to what mathematical thinking is and what kind of education best encourages it.In 2011, the psychologist Daniel Kahneman published Thinking, Fast and Slow, a book in which he explained for a general audience the main elements of the empirical work on decision making for which he had received the Nobel Memorial Prize in Economic Sciences in 2002. Kahneman's distinction between thinking fast and slow may help us better appreciate the main features of mathematical thinking. I shall give examples of mathematical thinking in elementary mathematics and discuss what - beyond the mathematics - we can learn from them.

## Lent 2015

 15th January, Singular Eigenvalue Perturbation Theory, Professor Barry Simon (Caltech) Eigenvalue Perturbation Theory is central to the theory of nonrelativistic quantum mechanics going back to Schrodinger's first papers. This lecture will review what is known about the eigenvalues in physical situations where one doesn't have simple convergence to a new isolated eigenvalue. Included are the anharmonic oscillator and Zeeman effect (divergent series and summability), autoionizing states in atoms (complex scaling and resonances), Stark effect (exponentially small resonances) and double wells (instantons). 16th January, Pizza and Board Games Night 23rd January, Distances, Sums and Products, Professor Béla Bollobás (DPMMS) Paul Erdös had an amazing ability to pose problems that are easy to understand, look innocent, perhaps even trivial, and are not only hard, but eventually also open up entirely new areas of mathematics. In this talk I shall present some of Erdös's favourite problems, and discuss recent developments. 29th January, No-three-in-a-line problems, Professor Ben Green (Oxford) Let S be a set in some vector space. What's the largest subset of S with no three collinear points? This simple question (for various choices of S) has led to some interesting mathematics touching on a diverse range of subjects from combinatorial number theory to algebraic geometry. I will discuss some of these topics from an elementary viewpoint. 5th February, Evolution of Biological Complexity, Professor Raymond Goldstein (DAMPT) It is a general rule of nature that larger organisms are more complex, as measured by the number of distinct types of cells present. Yet, increasing size has both costs and benefts, and the search for understanding the driving forces behind the evolution of multicellularity is becoming a very active area of research. In this talk, I will discuss the mathematics and physics underlying this biological problem. 15th February, Problems Drive Compete in pairs in this light-hearted contest in witty mathematics and mathematical wit. There will be various prizes for different achievements and light refreshments for all those who attend. 26th February, The self-avoiding walk problem, Professor Geoffrey Grimmett (Statslab) How many n-step self-avoiding walks exist on a given infinite graph? This question is easy to state but notoriously hard to answer. I will describe the history of the problem, and will summarise progress and open questions, one of which may seem quite elementary. 28th February, Annual Dinner, 7pm, Doubletree Hilton Hotel The Archimedeans cordially invite you to join us for our annual dinner on Saturday 28th February. This will be a three course meal with wine included, preceded by a drinks reception. We are delighted to announce that we will be joined this year by Professor Béla Bollobás, who will be our guest speaker at the event. Details Date: Saturday 28th February Timings: 7pm, Reception; 7:30pm, Dinner Location: Doubletree Hilton Hotel Map: here Price: £20 for members, £25 for non-members Payment Deadline: Friday 13th February Dress Code: Black tie preferred If you have any enquiries, please address them to the external secretary , with "Archimedeans Annual Dinner" in the subject line. 5th March, Eating and Racing, Professor Imre Leader (DPMMS) We'll consider some interesting finite games and some interesting infinite games.

## Michaelmas 2014

 9th October, Solving Analogy Problems with Letter Sequences, Professor Timothy Gowers Solving analogy problems with letter sequences, such as abc is to aabbcc as uvw is to ?? That's an easy problem, but there is a whole hierarchy of more and more interesting examples, and much of the talk would be about how to approach these problems systematically, which is challenging because every time you think you have a system, someone comes up with an analogy problem that has a natural solution that the system doesn't find. 10th October, How impossible is it to reconcile quantum logic with classical logic?, Professor Gerard 't Hooft (Utrecht) The properties of the tiniest particles of nature (atoms, molecules and sub-atomic particles), are described by the theory of quantum mechanics. Often, quantum mechanics is said to require a reconsideration of our rules of logic, as if "quantum logic" were something else. A theorem by particle physicist John Bell is then used to "prove" that no local, classical, deterministic theory can exist to explain quantum behaviour. However, there is reason to doubt whether that is true. Lecturer will demonstrate that systems exist that are classical and quantum mechanical at the same time. Our world of elementary particles, described by the "Standard Model", could be such a system, but how could it disobey Bell's theorem? 16th October, Endowed with an Extra Sense: Mathematics and Evolution, Professor Todd Parsons (France) Charles Darwin famously remarked "I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense." Despite this, the importance of mathematics (and contributions from mathematicians and statisticians from Cambridge in particular) for the development of the modern theory of evolution is largely under-appreciated. In this talk, I will survey the essential contributions mathematics has made to the development of the modern evolutionary synthesis, from the seminal work of J. B. S. Haldane, R. A. Fisher, and Sewall Wright, to John Kingman's coalescent, to the present. 23rd October, Pub Quiz N.A. 30th October, Knots and surfaces, Professor Ivan Smith A knot is an embedding of a circle into three-dimensional space. The study of knots, and of the surfaces that they bound, has surprising connections to three and four-dimensional topology, to numerous parts of algebra, and even to theoretical physics. The talk will give a brief introduction first to knots themselves, and then to some of these wider connections. 6th November, What mathematics tell us about the nature of life ... more than 3,800,000,000 years ago!, Professor Nigel Goldenfeld (UIUC) Relics of early life, preceding even the last universal common ancestor of all life on Earth, are present in the structure of the modern day canonical genetic code --- the map between DNA sequence and amino acids that form proteins. The code is not random, as often assumed, but instead is now known to have certain error minimisation properties. How could such a code evolve, when it would seem that mutations to the code itself would cause the wrong proteins to be translated, thus killing the organism? I address this paradox, originally due to Francis Crick, and show how dynamical systems theory leads to powerful insights about the nature of very early life that are beginning to be experimentally tested. 13rd November, How to solve a problem by making it harder., Dr. Vicky Neale Surprisingly, sometimes the way to make progress on a mathematical problem is to tackle a harder problem instead. I'll describe an example of such a problem from number theory. 20th November, The Geometry of Speech, Professor John Aston Comparative linguistics, which aims to understand the relatedness of languages, has traditionally been a qualitative discipline examining written records. In this talk, we'll attempt to persuade you that maybe a mixture of functional analysis, non-parametric statistics and non-Euclidean geometry, with the odd acoustic signal thrown in, might be another way to go. 27th November, Scope of String Theory , Professor Michael Green According to string theory the different sub-atomic constituents of matter - the electron, the quarks and other elementary particles - are to be thought of as different modes of vibration of an extremely small string. This simple postulate not only has the potential to unify the fundamental particles, but leads naturally to a consistent description of the physical forces. In recent times the mathematical structure of string theory has led to suggestions of how it might be applied to problems in areas of physics far removed from the ones it was originally intended for and that cannot be addressed by more conventional techniques. This talk will explain the background to the questions that string theory aims to address and give a non-technical description of properties of the theory. 4th December, The Mystery of Spinors, Professor Michael Atiyah Spinors play a fundamental role in physics and in several areas of mathematics. I will survey their history and their applications and I will delve into their deeper meaning. I will avoid technicalities.

## Easter 2014

 16th June, Science Societies' Garden Party, Pembroke We are delighted to invite you for the long-awaited, eagerly-anticipated, highly-contemplated 2014 Science Societies' Garden Party! It promises to be a fantastic afternoon, with plenty of food, drink and, who knows, perhaps even a few surprises... The participating societies are: Cambridge University Scientific Society (SciSoc) Cambridge University Physics Society (CUPS) Cambridge University Mathematical Society (Archimedeans) Cambridge University Astronomical Society (CUAS) Cambridge University Computing and Technology Society (CUCaTS) Cambridge University Biological Society (BioSoc) The Garden Party shall take place on Monday the 16th of June at Library Lawn, Pembroke College between 13:00 and 16:00. Prices: £5 - members online booking £7 - non-members online booking For a map, click here. Facebook event link. 11th June, Punting trip To celebrate the end of exams, the Archimedeans will be holding a punting excursion free of charge for members. The event will take place at 11am Wednesday 11th June at Trinity College Punts. Refreshments will be provided but you are of course welcome to bring your own. 2nd May, Board Games and Pizza Night Come along to the CMS this Friday, 6.30-8.30pm, for a Board Games and Pizza Night! We'll be in the Pav D common room with pizza, snacks, alcoholic/non-alcohol drinks and, of course, board games. Feel free to bring your own drinks and board games - especially board games! We need lots of board games. We'll be ordering pizza at 6.45pm so you should turn up before then if you're intending to eat pizza. Please bring £2 if you're a member or £3 if you're not. (A note on getting into the building: the doors should be open until 7.10pm, but if you arrive later someone will hopefully see you standing outside and let you in.)

## Lent 2014

 17th January, Number theory from Gauss to Langlands, Prof Tony Scholl (DPMMS) Abstract: On 18th April 1796, Gauss discovered his first proof of the famous law of quadratic reciprocity. I will describe some of the background to this striking theorem, and explain how it has led to the development of a huge area of mathematics, culminating in the "Langlands programme", a web of conjectures, mostly awaiting proof, linking aspects of number theory, geometry, representation theory and analysis. 24th January, The mathematics of aircraft noise and owls, Prof Nigel Peake (DAMTP) Abstract: Noise generation by aircraft (and onshore wind farms) is a big environmental issue. In nature, however, the owl has already solved the problem of silent flight. In this talk I will discuss some of the mathematics and physics of sound generation, and describe what we might learn from our feathered friends. 31st January, From images, corruption and resolution: a mathematical approach, Dr Carola Schoenlieb (DAMTP) Abstract: Restoring the original image contents from distorted measurements is one of the most important tasks in image processing. It comprises the enhancement and reconstruction of images distorted by noise or blur (image denoising/deblurring), the filling-in of gaps in images (image inpainting) and the reconstruction of an image from noisy (and possible undersampled) Fourier/Radon measurements. In this presentation we will discuss techniques from inverse problems, variational calculus and partial differential equations for the solution of some of these tasks. After spending some time on introducing the concept of such methods, some of their analytical and numerical challenges, we will get to know some recent advances in the field as well as challenges and open problems. All the mathematics you will see will be furnished with images from applications for image restoration, surface interpolation and MRI. 3rd February, Randomness and continuum, Prof Wendelin Werner (ETH Zurich) Abstract: One can have a rather intuitive perception of the fact that space and time can be continuous, which is very directly related to the mathematical notion of continuity of functions. On the other hand, when one thinks of random phenomena, the natural examples that first come to mind are of discrete nature, such as coin tossing. The conceptual question on how "randomness" can be split up into and reassembled from infinitesimal little pieces turns out to be quite tricky. It is related to contemporary research in mathematics that we shall illustrate via some concrete examples. 7th February, Supersymmetry at the Large Hadron Collider, Prof Ben Allanach (DAMTP) Abstract: I shall describe the dark matter mystery, and we shall go on a speculative journey to solve it. Going back to the beginning of time, we shall witness the birth of a proton, following it through to the present day, where it ends up in the Large Hadron Collider at CERN. We shall revisit the Higgs boson discovery from last year. Finally, we shall see show how the collisions between protons at CERN might give us vital clues to solve the dark matter mystery. 22nd February, Annual Dinner, 7pm, Doubletree Hilton Hotel The Archimedeans would like to invite you to join us for our annual dinner on Saturday 22nd February. With a drinks reception and a 3 course meal complete with wine, it's sure to be an excellent evening. Date: Saturday 22nd February Timings: 7pm, Reception; 7:30pm, Dinner Location: Doubletree Hilton Hotel Map: http://tinyurl.com/btj8umc Booking Link: link removed Price: £15 for members, £20 for non-members Booking and Payment Deadline: Thursday 6th February Dress Code: Black tie preferred We're pleased to announce that this year we will be joined by Dr. Vicky Neale (DPMMS), who will be our guest speaker at the event. You'll also have the chance to invite your favourite lecturer or supervisor to dine with us. We have set aside 15 places for such honorary guests, so please think carefully and use your invitation wisely. Payment details will be emailed to you automatically once you've submitted the form. Make sure you remember the payment deadline of Thursday 6th February. 7th March, Taylor's Theorem, Wrong On So Many Levels, Prof Tom Körner (DPMMS) Abstract: Of course, Taylor's theorem is both right (when correctly stated) and important. However, I shall try to convince you that it is a great deal more subtle than is generally believed.

## Michaelmas 2013

 14th October, Mathematics and the Simpsons, Dr. Simon Singh, 8pm, Bristol-Myers Squibb Lecture Theatre, Department of Chemistry Abstract: Simon Singh, author of Fermat's Last Theorem and Big Bang, talks about his latest book, which explores mathematical themes hidden in The Simpsons. Everyone knows that The Simpsons is the most successful show in television history, but very few people realise that its team of mathematically gifted writers have used the show to explore everything from calculus to geometry, from pi to game theory, and from infinitesimals to infinity. Singh will also discuss how writers of Futurama have similarly made it their missions to smuggle deep mathematical ideas into the series. 15th October, Geometry Through the Eyes of Physics, Prof. David Tong (DAMTP) 12-1pm, Cockroft Lecture Theatre, New Museums Site Abstract: Professor Tong will explain how ideas from quantum physics and string theory have resulted in new ways of thinking about the mathematics of geometry and topology. 15th October, Freshers' Squash, 1-2pm, Small Examination Hall, New Museums Site Meet new people, grab some free pizza, and of course, join the Archimedeans! 18th October, Solving Diophantine equations using invariant theory, Dr. Tom Fisher (DPMMS) Abstract: Classical invariant theory was something of an industry in the 19th century, first helping to create, and then being eclipsed by, modern abstract algebra. More recently the development of computer algebra has renewed interest in the classical explicit methods. I will explain how invariant theory can be used to help solve some problems in number theory. 25th October, How to Find (and Keep) a Wife, Dr. Paul Russell (DPMMS) Abstract: We consider applications of graph theory and combinatorics to the above problem. Hall's Marriage Theorem tells us when it is possible to marry off a group of men to a group of women in such a way that all are satisfied. But does there exist an algorithm to arrange the marriages in such a way that there will be no subsequent divorces? Yes, and it has been used in real life, but for the alternative purpose of assigning junior doctors to hospital places. If time permits, the talk will move on to generalizations of the above to civil partnerships. For anyone who finds the content of this talk of no interest whatsoever, please note that there is an isomorphic talk entitled "How to Find (and Keep) a Husband". 1st November, The Flying Trapezium Rule Prof. Nick Trefethen (Oxford) Abstract: The trapezoidal or trapezium rule for calculating integrals is sometimes spectacularly accurate, for example if the integrand is smooth and periodic. The mathematics of this effect is beautiful (the most powerful proof involves a complex contour integral), and the history is colourful (Poisson, Turing,...). The super-accuracy of the trapezoidal rule is the basis of the most powerful algorithms known today for certain problems of computational science. And is it related mathematically to the Faraday cage effect, where a wire mesh shields one almost perfectly from electromagnetic fields? 8th November, Hunter, Cauchy Rabbit and Optimal Kakeya Sets Dr. Perla Sousi (Statslab) Abstract: A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1928); we find a new connection to game theory and probability. A hunter and a rabbit move on the integer points in [0,n) without seeing each other. At each step, the hunter moves to a neighbouring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. The known optimal randomized strategies for hunter and rabbit achieve expected capture time of order n log n. We show that every rabbit strategy yields a Kakeya set; the optimal rabbit strategy is based on a discretized Cauchy random walk, and it yields a Kakeya set K consisting of 4n triangles, that has minimal area among such sets (the area of K is of order 1/log(n)). Passing to the scaling limit yields a simple construction of a random Kakeya set with zero area from two Brownian motions. (Joint work with Y. Babichenko, Y. Peres, R. Peretz and P. Winkler). 15th November, Board Games and Pizza Night CMS 6.30-8.30pm Come along to the CMS this Friday, 6.30-8.30pm, for a Board Games and Pizza Night! We'll be in the Pav D common room with pizza, snacks, alcoholic/non-alcohol drinks and, of course, board games. Feel free to bring your own drinks and board games - especially board games! We need lots of board games. We'll be ordering pizza at 6.45pm so you should turn up before then if you're intending to eat pizza. Please bring £2 if you're a member or £3 if you're not. (A note on getting into the building: the doors should be open until 7.10pm, but if you arrive later someone will hopefully see you standing outside and let you in.) 22nd November, Card shuffling and phase transitions, Dr. Nathanael Berestycki (Statslab) Abstract: Suppose you are given a deck with 52 cards. It is intuitive that if you shuffle it sufficiently many times, the order of the cards will be random uniform. But how many times is enough? It turns out that this apparently naive question reveals a deep and striking phenomenon: the deck of card experiences a transition between a phase where it is "far from random" and one where it is "very close to random". This is in fact very general and is analogous to the transition between the solid and liquid phases of water when the temperature passes 0C. The mathematics needed to describe this phenomenon will take us into a surprisingly large number of subjects, including probability, combinatorics, analysis, and representation theory. 29th November, Synchronization of Cilia, Prof. Raymond Goldstein (DAMTP) CANCELLED Abstract: From unicellular green algae to the lining of our respiratory systems are found hairlike appendages, known as cilia, whose coordinated beating results in transport of fluid essential for life. For decades there has been speculation about the origins of the synchronization seen in nature, but it is only recently that theory and experiments (mostly carried out here in DAMTP) have combined to provide quantitative analysis of this problem. This talk will describe the fascinating stochastic nonlinear dynamics underlying the synchronization problem.

## Easter 2013

 14th June, Science Societies' Garden Party, Library Lawn of Pembroke College. We are delighted to invite you for the long-awaited, eagerly-anticipated, highly-contemplated 2013 Science Societies' Garden Party! It promises to be a splendid afternoon, with plenty of food, drink and, who knows, perhaps even a few surprises... The participating societies are: - Cambridge University Scientific Society (SciSoc) - Cambridge University Physics Society (CUPS) - Cambridge University Astronomical Society (CUAS) - Cambridge University Mathematical Society (Archimedeans) The Garden Party shall take place on the Library Lawn of Pembroke College on Friday 14th June, between 1:30 pm and 4:30 pm. Prices: £5 - members online booking £7 - members on-the-door £7 - non-members online booking £9 - non-members on-the-door Tickets can be bought online here (link removed). Book now to avoid disappointment! If all the tickets are sold beforehand there'll be none left for the door... For a map, click here. Facebook event link.

## Lent 2013

 27th January, Undergraduate Symposium, 10am–6pm, MR2 Full schedule of talks The first ever undergraduate symposium of the Archimedeans will give students the chance to give talks to the society on their mathematical interests. 1st February, The Theorem of Archimedes, Prof. Sir Michael Atiyah (Edinburgh) Archimedes was very proud of his Theorem relating the surface area of a sphere to the area of a cylinder. He asked for this to be inscribed on his tombstone. Prof. Atiyah will show that his pride was justified and that his theorem has had a major impact on the mathematics of recent times, with surprising connections to such things as the isoperimetric inequality and the Hodge signature theorem. 9th February, Annual Dinner, 6.30pm, Doubletree by Hilton Please join us for our annual celebration of Mathematics at Cambridge. As usual, a reception and 3-course meal in sumptuous surroundings will be the backdrop for our social event of the year. We are lucky to be joined at the dinner by Prof. Imre Leader, who is the Senior Treasurer of the Archimedeans and will be our Guest Speaker for the night. In addition, this year we are giving you to opportunity to invite your favourite lecturers and supervisors to join us at the dinner. Book now before places run out! Map: http://tinyurl.com/btj8umc Price: £15 for members, £20 for non-members Booking link: link removed Booking and payment deadline: Thursday 24th January Dress Code: Black tie preferred 15th February, Conformal Geometry, its Beauty and Power in Physics and Cosmology, Prof. Sir Roger Penrose (Oxford) The ancient geometry of Euclid and its curved-space generalizations due to Gauss and Riemann are built upon a notion of (infinitesimal) distance. Somewhat less attention has been paid to the slightly more general geometry based simply upon the local notion of angle, referred to as conformal geometry. It involves many elegant theorems, and has direct applications to Einstein's special relativity and to Maxwell's electromagnetic theory. It is also central to a new view of the cosmological universe. 22nd February, Elliptic Curves, Prof. Kevin Buzzard (Imperial) Elliptic Curves can be thought of topologically as a torus, or algebraically as the solutions to a cubic equation in two variables. They have applications across mathematics, but as a number theorist Prof. Buzzard will stress the more arithmetic applications they've had in recent times, for example to the congruent number problem and Fermat's Last Theorem. He will also say something about the Birch-Swinnerton-Dyer conjecture, one of the most important unsolved problems in number theory. (Rescheduled from 18th Jan) 1st March, How to solve a linear equation?, Prof. Arieh Iserles (DAMTP) Our starting point is the familiar linear ODE system y' = A(t) y. How to expand the solution in a clever way? This innocent question will take us on a romp through graph theory, Lie algebras, group theory, numerical analysis and differential geometry. 3rd March, Problems Drive, 4pm-6pm, CMS Core Compete in pairs in this light-hearted contest in witty mathematics and mathematical wit. There will be various prizes for different achievements and light refreshments for all those who attend. 8th March, Secrets of Mental Maths, Dr. Arthur Benjamin (Harvey Mudd College) Dr. Benjamin is a mathematician and a magician. In his entertaining and fast-paced performance, he will demonstrate and explain how to mentally multiply numbers faster than a calculator, how to figure out the day of the week of any date in history, and other amazing feats of mind. He has presented his mixture of maths and magic to audiences all over the world. Arthur Benjamin is a professor of mathematics at Harvey Mudd College in Claremont, California. His TED talk as a mathemagician has been viewed over 5 million times. Reader's Digest calls him America's Best Math Whiz. 13th March, Annual General Meeting, 7pm, Winstanley Lecture Theatre, Trinity College Join us for a review of the past year, and to elect a new committee for the forthcoming year.

## Michaelmas 2012

 9th October, 12pm, Complex Sums in the Mathematical Tripos, Dr Stephen Cowley (DAMTP) Location: Cockcroft Lecture Theatre, New Museums Site, 12pm Join us for our first talk of term - the Freshers' Talk. Complex numbers appear throughout mathematics. Learn what they are all about, and how to study complex sums. 9th October, 1pm, Freshers' Squash, Small Examinations Hall, New Museums Site Meet new people, grab some free pizza, and of course, join the Archimedeans! 15th October, 1pm–5pm, Book Sale, CMS Core Come along to buy maths books at highly reduced prices, and have some squash and biscuits. 19th October, Did Galois deserve to be shot?, Dr Peter Neumann OBE (Oxford) Évariste Galois died aged 20 in 1832, shot in a mysterious early-morning duel. His ideas, after they were published fourteen years later, changed the direction of algebra and have had a huge influence on mathematics. In this talk we propose to explain something of his mathematical insights and legacy in non-technical terms, and why it seemed worthwhile to produce a meticulous bilingual edition of his writings. 26th October, Can you guess the next bit?, Prof. Andrew Thomason (DPMMS) If you are given a string of numbers (say, binary digits), can you work out the next one in the sequence? If you are the Minister of Education in search of bracing exam questions you will say yes, otherwise you will say no. Nevertheless, there are times when a sequence looks random but it is possible to say what comes next. We shall mention some real-life applications but by and large the talk is about simple, though sometimes unexplained, properties of numbers. 2nd November, 6:30pm, ‘Pub’ Quiz, CMS Central Core What better way to spend your Friday evening than to join us for a maths-themed pub quiz? Join up in teams and win prizes – a night of fun is a.s. guaranteed! Quotes on account of how quiz is not held in a pub. 9th November, Cambridge Impronauts Will it be a continuous night of laughter? Will the humour have no upper bound? Will there be any maths references at all? Only the Impronauts (formerly Improvised Comedy Ents) have the answer! 16th November, Bootstrap Percolation: Frivolous Questions and Daunting Problems, Prof. Béla Bollobás (DPMMS) Bootstrap percolation, introduced by Chalupa, Leath and Reich in 1979, is one of the simplest cellular automata. In the talk we shall present a selection of problems and results concerning it, from coffee-time questions to major results and unsolved problems. 23rd November, Do you know how much you know?, Prof. David Spiegelhalter OBE (Stats Lab) Your uncertainty can be quantified as a probability, but how can we tell whose probabilities are best? We will look at some theory of scoring rules for probabilistic predictions, and their applications in weather forecasting and other areas. And then we will measure your knowledge about your ignorance. 28th November, Scientific Christmas Party 2012, All Bar One, St. Andrews Street We're ending the Michaelmas term in style, with a Scientific Christmas Party co-organised by The Archimedeans, CUPS and SciSoc! The party will consist of a dinner buffet in All Bar One and is open only to members of any of the hosting societies - i.e. if you're not yet a member, but would like to attend the party, you need to become a member prior to your booking. Tickets are £13 drinking, £10 non-drinking. Book at http://tinyurl.com/xmas-party-registration, and pay via one of the following methods: 1. Cheque - Payable to 'The Archimedeans', send it to Colin Egan, Gonville and Caius College, with your name, CRSid/email and 'Scientific Christmas Party' on the back 2. Bank Transfer - Account Name: The Archimedeans; Sort Code: 40-16-08; Account Number: 20116386; please write your name and CRSid in the reference 3. Cash - pay an Archimedeans Committee member directly.

## Easter 2012

 15th June, 1pm, Science and Engineering Garden Party, Pembroke College Library Lawn. The Archimedeans are proud to co-host the Science and Engineering Garden Party, to be held on Friday 15th June from 1pm–4pm on Pembroke College Library Lawn. Benefits include: Food, including cheese. Pimms, as is traditional. Live music: The Funk Nuggets. They are a band. Pembroke has a map of their grounds; the Library Lawn is the lawn in front of the library. If you're still confused, the nice people at the Physics Society Wiki have rather more detailed instructions.

## Michaelmas 2011

 Tue 4th - Wed 5th Oct., Freshers' Fair, G1 main hall Location: Stall G1, Main Hall, Kelsey Kerridge Sports Hall, Queen Anne Terrace, Cambridge CB1 1NA Time: 10am to 6:30pm Tue 4th Oct and 10am to 3pm Wed 5th Oct Wed 12th Oct 12am, Freshers' Squash, St Columba's Hall, Downing Place Meet new people, grab a free lunch, and of course, membership at reduced prices. Fri 14th Oct, The National Curriculum Wars, Professor Martin Hyland (DPMMS) The UK is in the midst of a reform of the National Curriculum. Creating a Curriculum is hard work and the process creates high emotion: anxiety, anger and righteous indignation. I shall say a very little about that and shall use it as a starting point for the question what every mathematician coming to Cambridge ought to know. I shall propose a way to think about that in terms of what I regard as a special category of emblematic problems. I shall give examples from my own experience and reading but the main aim of the talk is to solicit further examples from the Cambridge mathematics community. Fri 21st Oct, ICE, Professor M. Grae Worster (DAMTP) Ice is one of the most powerful agents for environmental change on Earth. We are most aware of that in this country when we drive over potholes after a harsh winter. The same forces weather rocks, bring stones to the surface of fields and create landforms, particularly in regions of permafrost. The ice in arctic regions keeps our planet temperate both by storing heat between seasons and by reflecting sunlight. As the oceans freeze, dense brine is generated that drives large-scale circulations, of which the Gulf Stream forms a part. My talk will range over these phenomena, illustrating several of them with experiments, and introduce the ways in which mathematics can be used to make predictions. Sat 22nd Oct, 7pm, LCP informal employer presentation evening, Ramsden Room, St Catherine's College LCP is one of the UK's leading actuarial partnerships. We are looking to recruit up to 18 highly numerate individuals to train as actuarial consultants within our pensions, general insurance, investment and business analytics consultancies. Come and meet us for drinks and you will be able to experience why we have a reputation of being an exceptionally friendly and professional firm. You will also learn about work, the extensive training programme and what is it like to study for actuarial exams We will also be attending the Cambridge Careers for Mathematicians Event on 2nd November. Sat, 29th Oct, 7-9pm Board games evening! When: 7pm - 9pm Where: CMS Central Core Interested in a night of fun, food, and an opportunity to meet other mathmos? Come along to our games evening! Board and card games (including but not limited to: Set, Cluedo, Blokus and Balderdash) will be provided, but please do bring along your personal favourites. Snacks and drinks will also be supplied. Feel free to drop in for just a game or two, or better yet, come for the entire two hours! Free for members, £2 entry for non-members. Mon 7th Nov, 6-9:30pm, Jane Street Career Presentation Evening, Our staff will be on hand to speak to students and answer and questions they may have. Fri 11th Nov, 7pm, The Fundamental Theorem of Comedy, ICE - Improvised Comedy Ents Will it be a continuous night of laughter? Will the humour have no upper bound? Will there be any maths references at all? Only ICE has the answer! Location: MR2 in the Centre for Mathematical Sciences (CMS) Tue 15th Nov, Gloucester Research, Cormack Room, University Centre We are holding an evening presentation for Mathematics students in Cormack Room, University Centre, time TBA. Fri 18th Nov, Addictive Number Theory, Dr Vicky Neale (DPMMS) Apparently simple questions about adding whole numbers have led to some beautiful mathematics, involving ideas that at first sight seem to have nothing to do with the integers. In this talk, we'll get a flavour of this area, and we'll see how two great Cambridge mathematicians from the last century played a key role. We'll also see an application of the important fact that 1 is the smallest positive integer. Fri 25th Nov, Games of Pursuit and Evasion, Professor Imre Leader (DPMMS) A scorpion wants to catch a beetle, a porter wants to catch a student, and a lion wants to catch a man. The beetle, student and man do not want to be caught. What tactics should they adopt?

## Easter 2011

 13th June, Free Punting To bridge the time between exams and May Week, why not go punting while others are still sitting in the library? Meet at 10:45am, 13th June, at The Avenue (Trinity backs). The best thing about it? It's free for members! Refreshments will be provided. Places are limited, so please get in touch with the events manager (email) to reserve a place. 21st June, Science Societies' Garden Party, 14:00 - 17:00 Another year, another round of lectures, work, and exams. But with the end just over the horizon, we are excited to be able to offer the perfect antidote by inviting you all to the annual Science Societies' Garden Party! Come and relax with us in the sun* with a cool glass of Pimms and lots of delicious food. There will also be a Band and and non-alcoholic drinks for those already feeling pickled by May Week. Here are the details: Venue: Springfield Gardens, Harvey Court (Gonville and Caius College) - Along West Road from Queen's Backs. Click here for a map. Time: 14:00 - 17:00, Tuesday 21st June Price £3 / £5 Members/Non Members** - Pay on the door Hosted by: The Archimedeans, BioSoc, CUPS and SciSoc We look forward to seeing many of you there! Spaces at the Garden Party are unfortunately limited by capacity so make sure to arrive promptly to ensure a place. *Sun not guaranteed ** Members of The Archimedeans, BioSoc, CUPS or SciSoc