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.

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.)

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.

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.

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