School of
Mathematics,
University of Leeds,
Leeds LS2 9JT.
Tel: +44 (0)113 343 5130/1
Fax: +44 (0)113 343 5090
maths
excursions
-
2011/12 - semester 2
A series of entertaining
pieces of maths, light-hearted and accessible
to students at all levels and the general maths audience.
An initiative of the postgrad
students in the School of Maths. All are welcome!
Monday, 30th of April 2012, 2pm, Roger
Steven LT 04, Dr Kevin
Houston (Leeds) The Mathematics of Auto-Tune
Singers use Auto-Tune to ensure that they
are pitch perfect. This piece of software has had a huge impact on the
music industry and led to uproar when used on the X Factor. The talk
explains how it and popular console games such as Sing Star use
mathematics to produce their effects. Along the way we will try to
solve the puzzle of the Beatles' Magical Mystery Chord and discover if
you can hear the shape of a drum.
Wednesday, 14th of March 2012, 2pm, Leonard
Rogers Room (8.22d), level 8, School of Maths, Lee Zhuo
Zhao
(Cambridge) An Introduction to large deviation theory
An introduction to large deviation theory
The central limit theorem is one of the first important results
students encounter in a statistics course, although I would argue it is
a deep result of probability. One consequence of this theorem is that
the sum of a sequence i.i.d. random variables has an exponentially
decaying tail, just like the normal distribution. Large deviation
theory aims to explore the exact asymptotics of this decay and
therefore place a quantitative value on the probability of freak
events. In this talk I will try and motivate and introduce the theory
using only rudimentary results of probability and analysis and finally
show an application related to my research into branching processes.
Wednesday, 22nd of February 2012, 2pm, Roger Stevens LT 16,David
Bradley-Williams (Leeds) Number theory, secrecy and code breaking
Number theory,
group theory, computability and complexity theory are all strands of
mathematics which are depended upon for ensuring secrecy via
encryption, and for extracting other people's secrets through
cryptoanalysis. I will combine these strands to mention how mathematics
was used by the Allies to shorten World War II and by each of us every
day to protect our secret information. But why should we trust our
secrets are safe?
Wednesday, 1st of February 2012, 2pm, Roger
Stevens
LT 16, Richard
Elwes (Leeds) Pick's Theorem and Ehrhart Polynomials
Pick's Theorem is one of the jewels of
elementary geometry: a single, simple formula which determines the
areas of a huge range of shapes. We will also meet the more mysterious
Ehrhart Polynomials, which generalise Pick's theorem to shapes in
higher dimensions. These objects have many applications to problems in
computer science and optimisation.
2011/12 -
semester 1
Wednesday, 12th October 2011, 2pm, Roger
Stevens
LT 04, Imre Leader (Cambridge) Van der Waerden's Theorem
Lecture
slides
Suppose we are
presented with a long string of beads. The beads come in two colours,
red and blue, but there is not necessarily any pattern to the way they
are threaded on the string. Can we guarantee to find three
equally-spaced beads of the same colour? For example, if the 5th, 7th
and 9th beads were all blue then this would count. This question leads
to some beautiful mathematics.
Wednesday, 26th 2011, October 2pm, Roger Stevens LT 16,Cong
Chen(Leeds) Groups as Graphs
Lecture
slides
Given a group, we
can specify a list of generators and colours. Once we’ve done this we
can draw a map, like one of the Underground, of the group - because you
can get anywhere by following those generators. What do these pictures
look like, and what can they tell us about the group?
Wednesday, 9th November 2011, 2pm, Roger Stevens LT 18,Tina
Davies(Leeds) The solar magnetic field - what it looks like, what
it does, and how it might have got there
Just
like
the
Earth,
the
Sun
has
a
magnetic
field,
and
it
is
this
field
that
is responsible for the vast majority of both the features we see on the
Sun and the 'space weather' we experience on Earth. I will show
observations of solar features and explain how these match up with
magnetic activity on the sun, and then give an overview of the physics
behind what is happening and the current problems this poses for
theorists.
Wednesday, 16th November 2011, 2pm, Roger Stevens LT 16,Anastasia
Kisil(Cambridge) Acoustic problems, Wiener-Hopf method and rational
approximation
Many
real
life
problems
result
in
partial
differential
equations
(PDEs)
so
our
ability
to
solve
them
is important. There are no standard methods
that can solve all PDEs like there are for ordinary differential
equations (ODEs). In this talk I will talk about one beautiful method
of solving certain PDEs called Wiener-Hopf method. I will also
demonstrate how it can be useful in solving some wave propagation
problems.
Wednesday, 7 December 2011 2pm, Roger Stevens LT 06
- CANCELLED
DUE TO ILLNESS,David
Bradley-Williams(Leeds) Number theory, secrecy and code breaking
Number theory,
group theory, computability and complexity theory are all strands of
mathematics which are depended upon for ensuring secrecy via
encryption, and for extracting other people's secrets through
cryptoanalysis. I will combine these strands to mention how mathematics
was used by the Allies to shorten World War II and by each of us every
day to protect our secret information. But why should we trust our
secrets are safe?
2010/11
Wednesday, 2nd February 2011, 2 - 3pm,
Roger
Stevens
LT12 Stijn
Vermeeren (Leeds): Angel vs. Devil: a mathematical chase
The
Angel
flies
between
squares
on
an
infinite
chess
board;
every
second
he
can
fly
a
fixed
distance
k.
But
every
second
The
Devil
eats
one
square,
which
the Angel is not allowed to use anymore. Can the
Angel (if k is big enough) survive forever, or can the Devil always
trap the Angel by devouring all squares around him? This
simple-sounding question was an open problem for many years, and was
only resolved in 2006. Still, it is possible to sketch a solution
without using any advanced mathematics, which I will present to you.
The talk will contain many pictures and has a happy ending.
Wednesday, 16th February 2011, 2 - 3pm,
Roger
Stevens
LT12 Alexandra
Omar
Aziz (Leeds): Infinitesimals
I shall discuss the
concept of infinitesimals, infinitely small numbers, and explain how
their use can be given a rigorous mathematical foundation. After a
short historical introduction, I shall explain the model-theoretic
background underlying their construction and give some examples from
nonstandard calculus.
Wednesday, 2nd March 2011, 2 - 3pm, Roger Stevens
LT12 Dr
Mike Tehranchi (Cambridge): What is Brownian motion?
In
1827,
Robert
Brown
observed
the
random
motion
of
microscopic
particles
suspended
in
water.
Motivated
by
his
observations,
mathematicians
define
Brownian
motion
to
be
a
continuous
stochastic
process
with independent and stationary increments. Brownian motion is
central to probability theory since it is the key example of a Markov
process, a Gaussian process, and a martingale. This talk will explore
Brownian motion from these different perspectives, and indicate
applications to partial differential equations and complex analysis.
Wednesday, 16th March 2011, 2 - 3pm, Roger
Stevens
LT12 Dr
James
Cranch (Leicester): Maps between spheres
Some
mathematicians
think
that
the
set
of
maps
between
spheres
of
high
dimensions
is
an
object
more
fundamental
than
the
integers.
While
I
won't
have
nearly
enough
time to make that sound even remotely
sensible, I will be able to demonstrate why it's a topic that has
fascinated mathematicians ever since the 1930s, even though the state
of our understanding of the subject in 2011 is still laughably bad.
Wednesday, 23rd March 2011, 3 - 4 pm, Roger
Stevens
LT16 !!!
Different
time
and
room!!! Julian Mak
(Leeds):Mathematical Aspects
of Weather Forecasting, (With thanks to Dr. Keith Ngan, Met Office)
Although
essentially a problem in classical physics, the problem of
describing the dynamics of the atmosphere and ocean (both regarded as
fluids) are still far from being completely understood. In this talk, I
shall focus on the problem of modelling the dynamics of fluids via the
Navier-Stokes equations, an essential component in weather prediction.
The talk is split into two parts: first, how one would, ideally, solve
the equations and therefore obtain the dynamics; second, what people
actually do. This talk will also include a historical background on
weather forecasting, a brief history of the Met Office, and certain
details about the current weather / climate model employed by the Met
Office, known as the “Unified Model”.
