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General Audience Lectures

Further information can be obtained from the MIMS secretary.

Forthcoming Lectures

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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  • Wednesday 2 March
    2011
    The Galois Group - What's so special about the Golay codes?
    David Wilding (Manchester)

    1:10pm - 2:00pm - Alan Turing G-209

    Click here for the abstract

    An error-correcting code is a way of modifying digital information so that it is better protected against corruption. In this talk we'll look at a classic pair of codes, called the Golay codes, and we'll discuss their remarkable connection to combinatorics and finite group theory. The talk will be fairly non-technical and there'll be plenty of examples, so it should be accessible to all.

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