Abstract: The will be two parts to this last colloquium: The first part will be called "defend the indefensible". The object of this game is that someone will be given a topic to talk on for a minute (or thirty seconds), with the twist that the topic is "indefensible". For example, someone could talk on "why all PG students should be required to do extra tuition on Saturdays and Sundays" (or something possibly more interesting than that). With the person giving the best arguments winning a special prize. When we have volunteers, you can nominate topics for them to speak on. The second part will be the awards ceremony- there will be an award for best colloquium of the year and best cake of the year (and other, less serious ones), which might be a good thing to put on your CV. Voting for this will start after the last colloquium of the year is held next Friday.
Abstract: In an earlier colloquium I discussed the general relationship between geometry and knitting. This time I'll go through some examples of knitting projects, showing how knitting can be used to demonstrate mathematical concepts, as well as how maths can be used in knitting. But mostly I'll be showing off some things I've made. No previous knowledge of knitting, or the earlier `Geometric Knitting' colloquium is required.
Abstract: I'll give a primary school introduction to what a spinor is. It's often the case that people get bogged down in Clifford algebras and their classification that they give up before they find out what a spinor is, and I'll be very light on that. My old physics lecturers would say things like "a spinor is like the square root of a vector" without explaining what the hell they meant, so we'll see what they actually did mean in maths terms.
Abstract: This talk is a wild attempt to explain how to chop-up and classify Lie Algebras to complete beginners. Hopefully, I'll get to draw some root diagrams. So no fun this week then. In fact, 'wild' might be overselling it too. Given that it's such a big subject and I only have 30 minutes, I wont have time to explain how they arise as tangent spaces of certain manifolds (exciting) or even motivate their study, just how to chop. I'll assume that people know stuff about vector spaces, (like what eigenvalues are) and that they've heard the words Lie Algebra accompanied with some ugly looking gothic letters and wondered what they mean. It might be a little algebraic for some people, but algebra, like broccoli, is good for you."
Abstract: This talk will be of interest to people who would like
- to be able to win pub quizzes, or
- to learn Greek, or
- to find out what Scottish people discovered before the ancient Greeks, or
- to learn about the most prominent mathematical objects in my research, the reflection groups.
Abstract: Alexander Grothendieck was one of the best mathematical minds of the last century. His developments on Cohomology Theories and Scheme theory resulted in a coming of age for Algebraic Geometry. However, he is known as well for his radical political and philosophical ideas which resulted in an early retreat from the mathematical community and ultimately to a retirement in an unknown place in the Pyrenees. In this talk we will try to give an insight into his life and the Mathematics he develop in the fields of Analysis and Algebraic Geometry.
Abstract: If you have a Rubik's cube, please bring it along. I will show one method to solve the cube with only 4 algorithms that, although far from being the most efficient one, always works. I will also give a flavour of how this method is based on group theory.
Abstract: In this talk we introduce the concept of High Performance Computing. After a brief introduction, we illustrate the basics of message passing interface programming (MPI) using a simple program.
Abstract: The goal of this talk is to show that van Kampen's theorem is a special case of a `pushout'. In doing this, I hope to convince some of you that category theory can be (very) useful! I realise that people (unfortunately) may not be aware of van Kampen's theorem so I refer those of you to page 43 of the following book: http://www.math.cornell.edu/~hatcher/AT/AT.pdf I will review the statement of the theorem but my talk will pack little punch if you do not know the result in the first place (and in particular the fiddly arguments which are required to prove it). Otherwise you will just get some context-free categorical constructions which is no bad thing ;-)
Abstract: This talk will continue on the theme of Josef's talk from a few weeks ago. I'll give an accessible definition of the Bochner-Riesz multipliers, and the question we are interested in. We will then look at the partial answers which are known (mostly dating from the 70s) and what is still left unsolved. Hopefully along the way I will give a flavour of some of the tools and ideas which are important in my field, without getting too technical.
Abstract: Come to the colloquium this week to find out how a result in knot theory has managed to shed light on an old problem in number theory. There will be music, there will be audience participation, and hopefully there will be some 'oohs' at my nice formula!
Abstract: The first part of this talk will give a brief overview of the life of famous Scottish physicist James Clerk Maxwell, as well as introduce Maxwell's equations and describe some of their consequences. The second half of the talk will take a gentle look at a special case of Maxwell's equations from a nonlinear PDE perspective. This talk should be accessible to all.
Abstract: I will explain briefly the Nuclear Magnetic Resonance (NMR) features and why it is one of the most used spectroscopy technique, I then introduce the equation of motions for such a system, and generically for a specific type of quantum simulation and explain a couple of methods we have been developing to tackle some of the issues arising generally in quantum simulations.
Abstract: Compressed Sensing (CS) is a new paradigm in signal processing where we try to recover sparse signals from incomplete (a lot fewer than usual) measurements. Central in CS is the design of measurement/sensing matrices (such as Gaussian random matrices in which the entries are i.i.d normal) and the analysis of recovery guarantees of algorithms. A key property for checking these is the Restricted Isometry Constant (RIC) of the matrix, also known as the Restricted Isometry Property (RIP). However, calculating the RIC of a matrix is intractable deterministically hence the resort to probabilistic methods to derive RIC bounds. Using large deviation theory and set covering we derived the newest and best RIC bounds for Gaussian random matrices, so far. In the talk, I will start by introducing CS and RIC. Then I will state our bounds and discuss their implication for CS. I will conclude with a proof of the theorem of our bounds.
NOTE UNUSUAL TIME AND LOCATION.
Abstract: In the first part of the talk we will answer two questions of A. Besicovitsch and S. Kakeya. The answers will lead us in the second part of the talk to a surprising result of the 70s regarding the Disc Multiplier, which we will link to an open problem from nowadays, namely the Bochner-Riesz conjecture.
The talk is accessable to everyone (basic understanding of L^p spaces, Fourier Transform and Continuity of linear maps helps in the second part, but is absolutely not essential).
Throughout the talk there will be chocolately rewards for the motivated audience.
In this occasion there will be tea and cake BEFORE the colloquium at 4pm in the common room.
BONUS TALK: Lois Rolling on Research Communication in Action.
Abstract: I plan to introduce from scratch the notion of cellular homology with a view to stating the much celebrated Lefschetz fixed point theorem and several of its interesting consequences. This talk will be accessible to everybody.
There will also be a bonus talk at 3.30pm in which Lois will talk about the opportunities to take part in outreach activities while a postgraduate student. In particular she will explain the Research Communication in Action course which will run later this semester.
Abstract: I shall present in an accessible way some basic facts about Strichartz estimates - these are spacetime a priori estimates for the solutions to certain classes of linear Partial Differential Equations (PDE's) and have applications to proving existence of solutions to nonlinear PDE's. Examples shall include applications to models from Relativistic Quantum Theory and Biology.
NOTE UNUSUAL TIME, DAY AND LOCATION! Abstract: The association between mental illnesses and mathematics dates back to the beginning of time, and has extensively studied by several authors. In particular, the topical work of Prof. Nonnenmacher on the relation between men and lions has corroborated the theory that post-graduate students in mathematics are very likely to go mad. In this talk we shall investigate this intrinsic relationship using a number of examples: in particular, we shall also dwell on the question of the ability of deleting unwanted emails, which seems to escape at least one Ph.D. student every year (in spite of instructive lectures specifically aimed at curing this illness, e.g. Dr. Strothers' talk last year). Finally, time permitting, we shall explain the connection between recent developments and the foundational theory of marking which began with Professor Emeritus Urminsky, Chair of Complaints at the University of Edinburgh, and the Speaker at the First Achim Nonnenmacher Lecture Series. Requirements: Most concepts will be explained from first principles, but a sense of humour is needed. An extensive knowledge of random films and songs is preferable.
NOTE UNUSUAL LOCATION!
Abstract: Glider pilots in competitions have to try and find the fastest possible way of getting from A to B using only the power of the air. I'll be explaining the simple theory behind one possible strategy for doing this, and looking at what this means for a competitor. We'll also examine the basic geophysical features that help people stay in the air without use of an engine. In the absence of rigorous mathematics I hope to supply plenty of interesting pictures!
NOTE UNUSUAL DAY, TIME AND LOCATION! Programme:
There will be Cheese and Nibbles afterwards courtesy of ICMS.
Abstract: From his sick childhood, Joseph Pilates dedicated himself to rehabilitation and physical fitness. Joseph Pilates developed the Pilates Method which combines full body strengthening exercises with an Eastern paradigm. After Joseph Pilates death in 1967, his method was primarily used by dancers and athletes, but has recently become popular for people of all ages and backgrounds. Pilates is a mind-body exercise which focuses on strengthening the core postural muscles, while developing long lean muscles throughout the body, improving posture and increasing flexibility. We will introduce the fundamentals of the Pilates method and attempt some basic exercises. Note: This is an introduction to the pilates method and people will be expected to join in on basic exercises. Please wear loose clothing and bring a mat or towel if you're uncomfortable with lying on the floor.
Abstract: After the furore following the BNP leader's appearance on Question Time, I'll take a tongue-in-cheek look at some of the outrageous claims made by both the BNP and the Daily Mail with regards to immigration in Britain today, and the statistics that these claims are supposedly derived from.
Abstract: In this talk I'll describe what the "Monster group" is, how it fits into the classification of finite simple groups and give an outline of what the Monster moonshine conjecture is.
Abstract:I'll be giving a brief look at how to model a disease, using badgers and bovine TB as a real world example. I'll start by describing a simple deterministic SI model, and then show how we can use that to create a stochastic model. Some graphs and results may be present if time allows.
Abstract: Option contacts were first traded in the early 1970s and even today remain an highly used form of financial derivative. European options in particular demonstrate a closed form solution under certain stochastic models and as such have been extensively researched. In my talk, I shall introduce more exotic options, explaining how they compare to vanilla contracts, along with the challenges of finding an explicit solution for each.
Abstract: This talk is supposed to give a brief introduction to basic Galois theory, dealing with field extensions and their automorphism group. My aim is to discuss at least one of the classical applications of this, most likely the insolubility of the general quintic by radicals, trisection of angles or ancient Greek interior design.
Abstract: I'll be inviting a group of brave volunteers to describe their PhD research in the space of 2 minutes, and awarding FABULOUS PRIZES for the best presentations, as voted for by the audience. This should be fun, but does have a serious side -- making our research interesting and accessible to non-specialists is a challenge we all face at some point, whether it's attracting others to the area, obtaining funding or just seeing the 'big picture' or our own work. I'm hoping this colloquium will encourage us all to see our research from a fresh perspective. Also featuring Andrew Wilson as "Glamorous Assistant".
Abstract:We live in very fortunate times: everyone knows a metre is 100 cm and a litre is 1000 ml, but where do these come from? I'll be examining a (brief) history of units of measurement, starting with units used in Biblical times (including finding a surprisingly accurate estimate of Pi in the Old Testament) and why they were problematic, touching on the confusing world of imperial measurements and finishing by explaining where we get our modern metric units from.
Abstract: We discuss the solvability of the 2nd order parabolic Cauchy problem.
