General Audience Lectures

Forthcoming Lectures

• There are no current lectures planned, please check back soon for an updated list of forthcoming talks.

Previous Lectures

The Galois Group presents a talk from King Choo:

Wednesday 20th March 2013 1:00pm – 1:30pm
Alan Turing G.108

Tile: Chaos Theory

Abstract:
We will be introduce to a brief history of chaos theory- the change in mindset from certainty (Newtonian Mathematics) to uncertainty. The basic nature and idea of Chaos, its possible implications and why it's interesting.

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The Galois Group presents a talk from Prof Alexandre Borovik:

Wednesday 15th February 2012 1:00pm – 2:00pm
Alan Turing G.207

Tile: Eternity forever: Infinity in mass culture.

Abstract:

In my talk, I will try to explain the reasons behind the bizarre role of the concept of infinity in mass culture.

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The Galois Group presents a talk from David Wilding:

Wednesday 29th February 2012 1:00pm – 2:00pm
Alan Turing G.209

Tile: A Classical Conundrum.

Abstract:


What is the value of the greatest Roman numeral contained in 'LLIXILXLIVII'?

One way to calculate the answer is to use a mathematical device called an automaton.

In this talk I'll explain exactly what an automaton is and I'll construct one that answers the Roman numeral question.

I'll also discuss some of the practicalities of simulating automata with computers.

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The Galois Group presents a talk from Daniel Robinson:

Wednesday 7th March 2012 1:00pm – 2:00pm 
Alan Turing G.207

Tile:  A $10,000 Riddle.

The Riddle:

“100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Each day, the warden picks a prisoner equally at random, and that prisoner visits the central living room; at the end of the day the prisoner is returned to his cell. While in the living room, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?”

The talk will be more of a chat on how to solve the problem and various ideas on what is the optimal solution.


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The Galois Group presents a talk from Katie Steckles:

Wednesday 18th April 2012 1:00pm – 2:00pm
Alan Turing G.207

Tile: Zero-knowledge Proof Protocols

Abstract: Inspired by recently finding a nice research paper on the topic, I'd
like to introduce the concept of a zero-knowledge proof in
cryptography and give some examples of cryptographic and physical
protocols, which allow you to prove the truth of a statement, without
revealing any more information than necessary. Examples will range
from counting the leaves on a tree, via sudoku, to finding Hamiltonian
circuits in graph theory.

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The Galois Group presents a talk from Dr Hovhannes Khudaverdian:

Wednesday 25th April 2012 1:00pm – 2:00pm
Alan Turing G.207

Tile:  The Arithmetico-Geometric mean and the potential of the circle.

Abstract: For two numbers a,b ≥ 0 their arithmetic mean (a+b)/2 is
greater than or equal to their geometric mean √(ab). This is one of
the most ancient and most famous inequalities in mathematics.
      One may consider two sequences {a_n} and {b_n} such that
a_0 = a, b_0 = b and for every n, a_(n+1) and b_(n+1) are respectively
geometric and arithmetic means of the previous pair of numbers (a_n, b_n).
We come to two sequences of means {a_n}, {b_n}. These sequences have
a common limit Γ(a,b) which is called the arithemtico-geometric mean.
     This seems to be "l'art pour l'art". But Gauss introduced this notion
when trying to calculate the integral which gives the potential of the
circle on the plane at a point of this plane. It turns out that the
relation of this integral with the arithmetico-geometric mean gives an
excellent algorithm for easy numerical calculations of this integral.

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The Galois Group presents a talk from Connar Baird:

Wednesday 9th May 2012 1:00pm – 2:00pm
Alan Turing G.207

Tile: The AKS Primality Test.

Abstract:

The Agrawal-Kayal-Saxena theorem is the basis for a deterministic
primality test, which performs in polynomial time. The AKS primality test
is unique because the proofs needed to show that it is both fast and
deterministic do not rely on conjecture, unlike the popular Miller-Rabin
test which is deterministic on the condition that the General Riemann
Hypothesis is true.

The focus of this talk is to give a demonstration of the AKS test, to give
interesting quirks to how this procedure may be implemented, and to give
some ideas which may not be given in any normal number theory course.

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• Weds 16 Nov
  2011
  The Galois Group presents a talk from Prof Nick Higham:
  
  Alan Turing G.207
  
  Title: The Mathematics of Digital Photography
  
  
  

  Abstract:
  
  How does a digital camera capture an image?
  What is Jpeg?
  How can a digital image be made bigger, or smaller?
  What are colour spaces and which is the best to use when editing images on a computer?
  
  The answers to the these and related questions involve some fundamental
  mathematical tools---in particular, linear algebra, interpolation, nonlinear mappings,
  and fast transforms.
  I will give an overview of the mathematical aspects of digital photography,
  from capture through editing to output. I will conclude with some "before and after"
  examples of how mathematical thinking can help you to improve your images.

• Weds 9 Nov
  2011
  The Galois Group presents a talk from Prof Alexandre Borovik
  
  Alan Turing G.207
  
  Title: The Nature of Mathematical Intuition, Part 2.
  
  
  

  Abstract:

  What is mathematical intuition?
   
  The talk will address simple and basic questions of mathematical practice using simple everyday examples:
  •What is "mathematical intuition"?
  •What does it mean "to apply mathematics to solving real life problems"?
  •What is the "mathematical content" of various professional skills?
  The discussion will involve some example from psychology, history and ethnography.

  This talk is the continuation of the talk given on October the 19th and will include more strange and surprising stories

• Weds 26 Oct
  2011
  The Galois Group presents a talk from Amit Kuber
  
  Alan Turing G.207
  
  Title: Shadows in Discrete Hypercubes
  
  
  Abstract:
  
  One can think of the power set of a finite set as a poset with inclusion as partial order. This gives rise to a discrete hypercube which can also be thought of as a graph. We shall define the concept of the shadow of a subset of a level set of the hypercube which agrees with the geometric intuition. A famous theorem of Kruskal and Katona says that "the initial segment of colex ordering minimizes the lower shadow". We discuss this ordering and the theorem itself without proof, but with lots of examples.

• Weds 19 Oct
  2011
  The Galois Group presents a talk from Prof Alexandre Borovik
  
  Alan Turing G.207
  
  Title: The Nature of Mathematical Intuition.
  
  Abstract:What is mathematical intuition?
   
  The talk will address simple and basic questions of mathematical practice using simple everyday examples:
  •What is "mathematical intuition"?
  •What does it mean "to apply mathematics to solving real life problems"?
  •What is the "mathematical content" of various professional skills?
  The discussion will involve some example from psychology, history and ethnography.

• Wednesday 30 March
  2011
  The Galois Group - Is there any point in proving stuff, anyway?
  Dr Mark Kambites (Manchester)
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  The "P vs NP" problem is one of six remaining mathematical challenges for a solution to which the Clay Mathematics Institute is offering a $1,000,000 prize. At its heart is a fundamental question: is it really that much harder to solve a problem yourself than to check somebody else's solution?

  The field to which the problem belongs - computational complexity - is by the standards of mathematics still very young, and relatively little knowledge is needed for an intuitive understanding. Indeed it is one of the few major problems which could plausibly be solved by an enthusiastic amateur with a clever idea, rather than being the sole preserve of specialists with decades of experience. The talk will outline the problem, and try to explain why mathematicians, computer scientists and even philosophers get so worked up about it.

• Wednesday 16 February
  2011
  The Galois Group - Mathematical Connections in Nature
  Zhelyo Vasilev (Manchester)
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  Mathematics seems to be the language in which nature enables us to understand its intricacies. The quest of scientists to predict and understand the rules by which matter and space behave has lead to the creation and application of beautiful mathematical theories. As an example, we will concentrate on the developments on the law of gravitation and provide insights into the character of the General Theory of Relativity and explore the mystery of how non-Euclidian space geometry arises from the presence of mass.

• Wednesday 2 February
  2011
  The Galois Group - Codes to the Rescue
  Bogdan Banu (UVA/VU Amsterdam)
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  Error correcting codes were initially created to deal with the problem of data transmission through a noisy channel. Even if the first codes were based on simple, low-efficiency models, over time more powerful codes were developed, the best of them based on algebraic models. Today codes have many more uses, and one of them is in information security. In this talk, I'll illustrate how (algebraic) error correcting codes can be used to secure biometric data and to create encryption systems that are not breakable using quantum cryptography.

• Wednesday 8 December
  2010
  The Galois Group - Prime (dys)function
  Dr Charles Walkden
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  Prime numbers have many practical uses. Wouldn't it be useful to have a convenient, simple, formula that generated arbitrarily large primes? In this talk, I'll describe some rather attractive formulae for primes - and then, in a tour around some associated results/conjectures in number theory (including the Riemann hypothesis), point out why they aren't so useful for practical purposes... I'll also give a light-hearted look at some famous former Manchester mathematicians who have worked on related problems. Everybody is welcome, and the talk will be accessible to all, including 1st year undergraduates.

• Wednesday 24 November
  2010
  The Galois Group - Quantum Computing
  Dr Richard Banach
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

• Wednesday 10 November
  2010
  The Galois Group - The Brouwer Plane Theorem and Its Applications
  Simon Baker
  
  1:10pm - 2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  Dynamical Systems like many areas on Mathematics is particularly useful in the way it interacts with other fields. Building on from ideas in Dynamical Systems we can prove what was one of the most important unsolved problems in Differential Geometry. In this talk I intend to give an outline of the steps involved. Firstly showing how the humble Brouwer Plane theorem proves Poincare's last geometric theorem and then finally we use what we have shown to give an argument for the proof of the Klingenberg conjecture.

• Wednesday 27 October
  2010
  The Galois Group - Scaling and Dimensional Analysis
  Prof Alexandre Borovik
  
  1:10pm - 2:00pm - Alan Turing G-108
  
  
  Click here for the abstract

  Dimensional analysis is a familiar tool for physicists and engineers, but in fact it is a neglected chapter of elementary mathematics which provides an unifying approach to a variety of mathematical phenomena and allows us to see, at a glance, a qualitative behaviour of objects in physics and mathematics. I'll give a brief history of dimensional analysis, from Galileo to Kolmogorov, illustrated by plentiful very elementary examples.

• Wednesday 28th April
  2010
  The Galois Group - Maths and Music + Rowlan Willis, the Fabric of the Universe
  Tom Harrison
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  TO FOLLOW

• Wednesday 21st April
  2010
  The Galois Group - Category Theory
  Pouya Adrom
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  The language of category theory generalises abstract notions encountered in diverse areas of mathematics. Starting with simple objects, it provides powerful concepts that can express complicated ideas concisely and, despite their highly general nature, are rather easy and intuitive to handle. Although a relatively new discipline, application of its terminology is ubiquitous, and it is an active area of research in itself and expanding in influence within other areas. This talk will introduce the fundamentals of the theory and try to indicate its significance and power to unify and illuminate structural similarities across different subjects.

• Wednesday 17th March
  2010
  The Galois Group - Involutions in Finite Groups
  Prof Peter Rowley
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  An involution in a finite group is an element of order two. Or, equivalently, an involution is a non-identity element which is equal to its own inverse. For a finite group its involutions can have a considerable influence upon the structure and properties of the group - the case when the group has no involutions at all being particularly noteworthy. The famous Brauer Fowler theorem and its impact on the simple group classification will also be discussed.

• Wednesday 3rd March
  2010
  The Galois Group - A Prime Puzzle
  Martin Griffiths
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  We all know, hopefully at least, that the arithmetic progression 8, 12, 16, 20, 24, … contains no primes whatsoever, whilst 1, 3, 5, 7, 9, … contains infinitely many. What about 3, 7, 11, 15, 19, … ? It turns out that, as with the previous sequence, it is straightforward to show that this contains infinitely many primes. It is possible to deal with a number of other special cases using, for example, the Euler- Fermat theorem or properties of cyclotomic polynomials. However, Dirichlet’s theorem on primes in arithmetic progressions, one of the crowning glories of nineteenth-century number theory, allows us to dispense with all these ad hoc methods. It tells us precisely when there is an infinitude of primes in an arithmetic progression. We discuss an elementary proof of this wonderful theorem.

• Wednesday 24th February
  2010
  The Galois Group - The Great Depression vs the Current Recession
  Krisjan Korjus
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  Economic crises are a complicated phenomena which can over-throw currencies and countries. How should we study them? What happened before and after the Great Depression and what can we learn from it? There is lots of information available, but it’s hard to fit it into a coherent picture. What is worse, most of the analysis done by financial banks or politicians is biased and narrow minded. I will show you some different graphs of socioeconomic data which reveal some cool relationships within our complex society.

• Wednesday 29th April
  2009
  The Galois Group - Linux for Mathematicians and A Group Calculator to help in learning Group Theory
  John Reynolds and John Coffey
  
  1:10pm - 2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  Linux for Mathematicians - Drawing on approximately twenty years experience in writing and maintaining software in various aircraft stress offices, I intend to discuss why I believe programming skills are likely to be very useful to any mathematician who works with numbers. I shall consider a few topics which are of interest to individuals rather than to employers, and show that computers allow mathematicians to get results which, a few years ago, would have needed large teams of people. I shall also discuss the Linux operating system, and its support groups, as I believe this provides a suitable environment for people wishing to develop computer skills without relying on an employer.
  
  

  Click here for the abstract

  A Group Calculator to help in learning Group Theory - As an undergrad trying to grasp what symmetry groups are all about, I would have found it useful to have an easy group theory calculator to experiment with simple examples of groups. When I could not find a suitable program on the Internet, I set about writing one to teach myself basic group theory. Other students might find this a helpful study aid, so the talk will outline what the Calculator does. You can download it, plus fully worked examples, from www.mathstudio.co.uk.

• Wednesday 18th March
  2009
  The Galois Group ? Paradoxical Decompositions
  Professor Richard Sharp (School of Mathematics)
  
  1:10pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  It is possible to decompose a solid sphere into a finite number of pieces, which may be rearranged to make two spheres each with the same volume as the original one. Put more informally, it is possible to cut an orange into a finite number of pieces and reassemble them into two oranges of the same size. This is called the Banach-Tarski paradox and is perhaps the most counterintuitive of a family of so-called "paradoxical decompositions". This talk will explain some of the mathematics involved, exploring concepts of volume, non-measurability and self-similarity.

• Wednesday 4th March
  2009
  The Galois Group - The Dark Ages: Mathematics in Decline?
  Phil Brockway (School of Mathematics)
  
  1:10pm - 1:35pm - Alan Turing G-205
  
  
  Click here for the abstract

  From the relentless barbarian invasions of Western Europe throughout the fifth century until the "rebirth" of learning in the eleventh century we have a period known as the Dark Ages. It traditionally marks a low point in the development of mathematics amidst social meltdown and cultural stagnation. In the west, the Christian Church became the custodian of mathematics in the few monasteries where learning still occurred. The (eastern) Byzantine Empire remained independent and isolated for nearly one thousand more years, and here classical Greek mathematics was preserved. However, as new religious observances swept through Europe and the middle-east in 622 under the Islamic caliphate, the necessity for cohesion in Islamic practise produced new methods of problem solving. In particular, the Islamic law of inheritance serving as the impetus behind Al-Khwarizmi's extensive work in the development of algebra.

• Wednesday 4th March
  2009
  The Galois Group - Darwin's Legacy Or How to Build a Family Tree
  Nawal Husnoo
  
  1:35pm - 2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  I will give a short introduction to the Theory of Evolution by Natural Selection and a brief description of how to build an evolutionary tree based on DNA analysis and the molecular clock.

• Wednesday 18th February
  2009
  The Galois Group - Large Primes and Very Large Numbers
  Roger Plymen (School of Mathematics)
  
  1:10pm - 2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  This talk is about the distribution of prime numbers. The law which controls the distribution says that the average spacing between primes around any natural number x is log x. For very large values of x, unexpected things start to happen to the spacing between primes. The original Skewes number 10^(10^10^10^3) was an attempt to pin down where this happens. We will discuss more recent attempts to reduce the Skewes number. The numbers remain very large. Riemann's formula relates a sum over primes to a sum over the zeros of the Riemann zeta function. This will be a big part of the story.

• Wednesday 17th December
  2008
  The Galois Group - Mathematics and philosophy - How do these subjects differ?
  Sam Savage (School of Mathematics)
  
  1:10pm - 2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  Can we pose philosophical questions mathematically in order to come to conclusive answers? This lecture will examine various philosophers', physicists' and mathematicians' relatively recent attempts and successes at answering bold philosophical and often seemingly ambiguous questions. The lecture will look at the paradoxes of self referential statements such as "I am a liar", including the possibility of time travel, philosophically, physically and (most importantly!) mathematically. The lecture will mainly explore Max Tegmark's mathematical formalization of a theory by David Lewis that states "every logically consistent universe exists" and its implications for philosophy and physics. I will try to explain how this can characterise the notion of objectivity which is essentially Group theoretic.

• Wednesday 3rd December
  2008
  The Galois Group - From Perspective to the Projective Plane
  Dr. Peter Eccles (School of Mathematics)
  
  1:10pm - 2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  During the fifteenth century artists made significant advances in the use of perspective in order to give an impression of depth in their pictures. Leon Battista Alberti wrote the first text on this subject in 1435. I will describe his method for drawing a square tiled pavement and illustrate it using a photograph of the Alan Turing Building taken by Nick Higham. Alberti's work led to questions about what geometrical features different views of the same object might have in common. The answer to this question was provided by Girard Desargues in 1639 with the introduction of projective geometry. In this, additional 'points at infinity' are added to the Euclidean plane so that any pair of straight lines in the plane meet at a unique point (which is a point at infinity if the lines are parallel). This feature is observed when viewing straight railway lines going into the distance: they appear to meet at a point at infinity. I will give an example of how Desargues was able to unify certain disparate results in Euclidean geometry, by observing that they are all special cases of a single result in projective geometry. In more modern times, topologists have studied the projective plane as a single object in its own right. In 1902, Werner Boy constructed a model of the projective plane in three dimensional Euclidean space. I will describe one method for constructing this model. I will also mention some unsolved problems relating to models of this type.

• Wednesday 12th November
  2008
  The Galois Group - Bootstrapping - Not just securing your footwear!
  Pete Green (School of Mathematics)
  
  1:10pm - 1:35pm - Alan Turing G-207
  
  
  Click here for the abstract

  Ever needed more data than you were able to collect? Ever needed to solidify some statistics or create confidence intervals with a small sample size? Then bootstrapping your sample could be a very useful solution! Third-Year student Pete Green gives a basic introduction to this simple, but powerful Monte Carlo sampling method, along with some real-life applications and worked examples!

• Wednesday 12th November
  2008
  The Galois Group - Building a machine that makes money!
  Kristjan Korjus (School of Mathematics)
  
  1:35pm - 2:00pm - Alan Turing G-207
  
  
  Click here for the abstract

  Kristjan is going to talk about a machine that beats the stock market! He will try to explain the concept of financial modelling and also touch on topics such as money, ethics of financial markets, genetical algorithms and MatLab. There will be discussion of the theory behind making this machine along with some of the issues he encountered while working on the project. In the end you should get some interesting ideas about money and our society with recommended articles for further reading.

• 15th October
  2008
  The Galois Group - Categorification
  Prof. Nige Ray (School of Mathematics)
  
  1:10pm-2:00pm - Alan Turing G-107
  
  
  Click here for the abstract

  Thousands of years ago, when people were learning to count their sheep (amongst other things!) the process of decategorification was seen as a stroke of genius, that allowed the development of number. During the last 30 years, it has dawned on mathematicians and theoretical physicists that the time has come to reverse this process, and work through ideas that had never been properly developed beforehand, but which are just as fundamental to mathematics as counting. In its own language, categorification involves replacing sets with categories, functions with functors, and equations with natural isomorphisms. I shall try to make some sense of this for a general mathematical audience.

• 7th June
  2008
  The Galois Group - How America Chooses Its Presidents
  Dr Alex Belenky (MIT)
  
  5pm - Alan Turing Frank Adams 1
  Summary (2 pages) of the lecture.

• 7th May
  2008
  The Galois Group - Mathematics in Industry
  Prof. Bill Lionheart (School of Mathematics)
  
  1:10pm-2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  How does mathematics help in practical problems in industry and commerce? How do mathematicians work with industry? What job opportunities are there for maths graduates where they will use their mathematical skills?
  
  I will illustrate the answer to this with some examples of work I have done with industry including such things as diverse as helping a steel mill, devising new types of computer display, improving medical imaging and working on airport security. I will tell you about some maths graduates I know and the work they do, and some of the impact of maths in our daily life.

• 23rd Apr
  2008
  The Galois Group - Geometry from Euclid to Hilbert
  Pouya Adrom (School of Mathematics)
  
  1:10pm-1:35pm - Alan Turing G-205
  
  
  Click here for the abstract

  The Euclidean approach to geometric exposition, as illustrated in his Elements', predominated mathematical thinking and pedagogy for more than fifteen centuries. However, new developments in other fields, especially algebra and analysis, soon led to emergence of new methodologies in studying geometry (geometries!).
  
  This talk will briefly survey the conceptual history of geometry up to the publication of David Hilbert's 'Foundations of Geometry'.

• 23rd Apr
  2008
  The Galois Group - Solving Chess
  Mehregan Ameri (School of Mathematics)
  
  1:35pm-2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  In February 1996, a chess game between Deep Blue, IBM's infamous chess-playing computer, and Garry Kasparov, the World Champion at the time, proved for the first time that machines are capable of beating even the strongest human. In a rematch a year later, Kasparov started the game with an irregular opening tactic, hoping to throw off the computer so to speak. The game was drawn. Clearly Deep Blue was not playing a perfect game. However, the question remains: Is it possible for a computer to play a perfect game of chess? Or even better, does there exist a pure strategy (i.e one that provides players with specific moves to follow at each step)?
  
  In this talk we will look at mathematicians' progress in solving chess and the attempts to create a chess-playing machine.

• 12th Mar
  2008
  The Galois Group - Navigation on the Riemann Sphere
  Professor Sasha Borovik (School of Mathematics)
  
  1:10pm-2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  Seafarers of 16th century were skillful in keeping course of constant direction - with the help of a magnetic compass and astronomic instruments - but they had no control over distance travelled since they had no control over the strength of wind. In effect, they lived in a strange geometry where only angles mattered, but which was lacking the concept of distance. Nowadays this geometry is known under the name of conformal geometry. The best way to understand it is to view the globe as the Riemann sphere invented by Bernhard Riemann (1826-1866) as a geometric model for representation of complex numbers.
  The famous geographer and cartographer Gerard Mercator (1512-1594) has not left us any clues as to how he made his world map of 1569; but it was the first map in the history where lines of constant direction on the globe (loxodromes) were represented as straight lines (rhumb lines, in seafaring terminology) on the map. The first systematic theory of Mercator's projections appeared some years later, in Edward Wright's book of 1599. However, Wright's work created more mathematical mysteries than mathematicians of that time could resolve.
  In my lecture, I will discuss some elementary and exceptionally beautiful mathematics related to the Mercator projection and Riemann sphere. In particular, I will explain why the Mercator projection is exactly the logarithm function Log(z) in the complex domain.
  
  My lecture is based on ideas of our colleague Dr Hovhannes Khudaverdian.

• 27th Feb
  2008
  The Galois Group - Rubik's Cube: A Permutation Puzzle
  Jake Goodman (School of Mathematics)
  
  1:10pm-1:35pm - Alan Turing G-205
  
  
  Click here for the abstract

  The Rubik's Cube is an iconic mechanical puzzle from the 1980's that is interesting mathematically as it admits a natural group structure offering a tangible example of a large permutation group (subset S₄₈ ). In this talk, we shall discuss some basic properties of the so-called "Rubik's Cube Group" and see how solving the puzzle essentially involves calculating an inverse element in terms of 6 particular generators.

• 27th Feb
  2008
  The Galois Group - The Agony and the Ecstasy - Mathematics and Art
  Hala Sabri (School of Mathematics)
  
  1:35pm-2:00pm - Alan Turing G-205
  
  
  Click here for the abstract

  Surrealism or Impressionism, illusions or the Renaissance, calligraphy or tiles - whether you look at fine pencil sketches or deep paintbrush strokes or spiralling whorls of colour, hiding right behind, you'll find Maths. Artists use it to show an honest reflection of life or they might paint the mathematically impossible in order to create an alternate reality or occasionally the painting might just be an allegory for Maths. Whether embracing it or rejecting it or hiding it, all artists rely on Maths, and here's hoping to uncover it in this talk!

• 13th Feb
  2008
  The Galois Group - Tube Formula
  Dr Hovhannes Khudaverdian (School of Mathematics)
  
  1:10pm-2pm - Alan Turing G-205
  
  
  Click here for the abstract

  Consider a stadium which has the form of a rectangle with perimeter P. Then the area of a running track of width h of this stadium is equal to S(h)=Ph+π h².
  
  It is a beautiful exercise to check that this formula also holds for an arbitrary convex polygon. We consider the generalisation of this formula for curves, polytops and arbitrary surfaces. It turns out that the n+1-volume of a running truck-tube of width h over an n-dimensional surface is a polynomial over h of order n. What is the geometrical meaning of coefficients of this polynomial?

• 12th Dec
  2007
  The Galois Group - Monster Maths!
  Dr Louise Walker (School of Mathematics)
  
  1:10pm-2pm - Alan Turing G-209
  
  
  Click here for the abstract

  Groups are algebraic structures that can be used to study symmetry and many other important concepts in mathematics. Just as prime numbers are the building blocks of the natural numbers, finite groups can be constructed from special objects called simple groups.
  This talk will explain what is meant by groups and simple groups and describe the fascinating quest to find all finite simple groups, including the Monster group!

• 28th Nov
  2007
  The Galois Group - The "true account" of Galois' life, and about the Group
  Shahzia Hussain (School of Mathematics)
  
  1:10pm-1:30pm - Alan Turing G-209
  
  Click here for the abstract

  Everyone has agreed with the fact that the young French mathematician Evariste Galois had a life riddled with misfortunes and injustice. However, the true account of his life has become but a mystery due to many authors (for example ET Bell, L Infeld and F Hoyle) fictionalising the real events that occurred. This talk will present two accounts of Galois' life, each as "believable" as the other! The talk will conclude by discussion of The Galois Group

  28th Nov
  2007
  The Galois Group - Early Mathematics
  Katherine Warren (School of Mathematics)
  1:35pm-2:00pm - Alan Turing G-209
  
  
  Click here for the abstract

  Ever wondered about the mathematics behind the pyramids? How the Mayan calendar worked? Or how modern maths began? The talk is an introduction to the mathematics in the Ancient world, how they are interlinked and how they influenced the way we study mathematics today.

• 14th Nov
  2007
  The Galois Group - Life in a Two-Dimensional Universe
  Dr Colin Steele (School of Mathematics)
  
  1:10pm-2pm - Alan Turing G-205
  
  
  Click here for the abstract

  In 1885, Edwin Abbott published a book called 'Flatland' which was about a two-dimensional world. The 'hero' was Mr A Square and other inhabitants included triangles, hexagons etc. Other authors have produced different variations on a two-dimensional universe. Such universes can be extended to include astronomy and this talk considers what astronomy would be like in a 2-dimensional universe. One significant change is that gravity is not inverse-square but is instead simply inversely proportional to distance. The shapes of orbits are different as a result. This talk will consider many aspects of astronomy in a 2-dimensional universe including orbits, seasons, eclipses, meteors, aurora etc. The talk will conclude by considering universes with alternative numbers of dimensions, 4-dimensional, 1-dimensional and 0-dimensional. It can be concluded that, other that the 3-dimensional universe,the two-dimensional is most interesting.

• 18th Apr
  2007
  The Galois Group - Mathematics and Celtic Art
  Michael Brennan (Waterford Institute of Technology)
  
  1pm - Newman G15
  
  
  Click here for the abstract

  Should the Time Team consult a mathematician whenever they uncover a Roman mosaic? Did the Vikings who trod the road past Manchester on their journeys between Dublin and York discuss tessellations of the plane? And do we need a little know theory to get the best out of the ornament in the great monastic books of Lindisfarne and Kells?
  In short, were our Celtic, Anglo-Saxon and Viking ancestors as brainy as us? These and other questions will be considered in this seminar talk in which simple logic will be applied to a first millennium art form, with relevance to art history, archaeology and mathemayics.

• 24th Oct
  2006
  The Galois Group - Come and get pent-up!
  Dr Sara Santos (Manchester Grammar School)
  
  1pm - Chemistry G53
  
  
  Click here for the abstract

  In the talk I will go through all the pentominoes: give the audience sets of 5 squares and ask them to come up with all the shapes. I will explain symmetry like reflection and rotation and ask if they can be matched like a jigsaw in a rectangular shape. The talk will also cover general ominoes and look at what happens in 3-dimensions.

• 8th Mar
  2005
  The Galois Group - Vedic Mathematics
  Dr Jitesh Gajjar (University of Manchester)
  
  1:00pm - Newman G15
  
  
  Click here for the abstract

  Vedic mathematics is a system of mathematics devised by the Indians for doing fast calculations. This talk will explore the origins and describe some of the magical techniques one can use for doing fast mental arithmetic. Are you ready for the Vedic Maths challenge?

• 23rd Nov
  2005
  The Galois Group - Packing Oranges in 24 Dimensions
  Dr. Louise Walker (University of Manchester)
  
  2:00pm - Room D7, Renold Building
  
  
  Click here for the abstract

  In this talk we'll start by looking at the problem of packing spheres in 2 and 3 dimensions. We'll then extend these ideas to higher dimensions and discover that something special happens in 24 dimensions. We'll also look at how these ideas relate to groups, codes and crystal lattices.

• 12th Oct
  2005
  The Galois Group - The Gambler's Tale
  Professor David Broomhead (University of Manchester)
  
  1:00pm - Rutherford Lecture Theatre - Schuster Building
  
  
  Click here for the abstract

  Some time ago the BBC reported that the probability of the Earth suffering a major impact with a large meteor is greater than the probability of winning the jackpot in the National Lottery. Leaving aside the interesting question of why, each week, millions of us spend their money playing the Lottery, this talk will discuss why the outcome of the Lottery draw is assumed to be so random. Isn't there a problem with this? Don't the Lottery balls satisfy Newton's Laws of Motion? Why, then, hasn't an unscrupulous mathematician made a killing by solving the equations on a computer? Selflessly dragging himself away from an important computer programming project, the speaker will discuss such questions as: what do we mean by a `random number'?, how do certain seemingly innocuous equations give complicated---chaotic--- solutions? He will also confirm the rumour that random equations can give rise to rather beautiful, ordered, structures.