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Tuesday, June 8, 1600-1700 |
Speaker :
Staffan Rodhe, Uppsala.
Title : Samuel Klingenstierna - 1700-talets
viktigaste svenske matematiker.
Abstract
:Samuel
Klingenstierna ar en tidig foretradare for den svenska vetenskapliga
revolutionen under 1700-talet. Mycket pa grund av sin ovilja att publicera sina
skrifter har han kommit i skymundan gentemot de mer kanda vetenskapsmannen
Carl von Linne, Anders Celsius och Torbern Bergman. Emellertid var
Klingenstierna aven en internationellt mycket valkand matematiker. Han hade
mott och/eller brevvaxlat med alla de stora matematikerna fran sin samtid
som Johan Bernouilli, Clairaut, Cramer och Euler. Foredraget kommer att ge en
beskrivning av hans liv och peka pa flera av hans vetenskapliga resultat.
Vidare kommer hans losning av det utokade brakystokronproblemet, med en kropp
som faller i ett resistent medium, att visas. Losningen till detta problem ar
Klingenstierna troligen forst med att genomfora, nagra ar fore Euler.
|
Monday, May 3, 1600-1700 |
Video Presentation : Fermat's Last Theorem.
Abstract
: BBC Horizon
documentary from 1997 charting the history of Fermat's Last Theorem, in
particular the modern history starting from the Taniyama-Shimura-Weil
conjecture (mid 1960s), the proof of which for 'most' elliptic curves
by Wiles (1994) eventually yielded the final solution to Fermat's puzzle.
The program contains interviews with Wiles, Shimura and several other leading
number theorists. I think I'm in it too (though not in the role of 'leading number theorist') !
OBS! The talk originally scheduled for today had to be cancelled but may take place instead at a later date.
|
Monday, May 10, 1600-1700 |
Speaker : Professor Roman
Shterenberg, KTH and
Mittag-Leffler Institute.
Title : Periodic magnetic Schrodinger
operator with degenerate lower edge of the spectrum.
Abstract
: We
investigate the structure of the lower edge of the spectrum of the periodic
magnetic Schrodinger operator. It is known that, in the non-magnetic case, the
energy is a quadratic form of the quasi-momentum in the neighbourhood of
the lower edge of the spectrum of the operator. We construct an example of the
magnetic Schrodinger operator for which the energy is partially degenerated
with respect to one of the components of the quasi-momentum.
|
Tuesday, April 13, 1600-1700 |
Speaker : Professor Susan
Montgomery, University of Southern California and
Mittag-Leffler Insitutet.
Title : From groups to Hopf algebras.
Abstract
: In this talk I will report on some recent work, and some not so recent, on what is known about the classification of finite-dimensional semisimple Hopf algebras over the field of complex numbers. This case has much in common with classical results about finite groups; for example, a basic tool is the analog of Lagrange's theorem that the order of a subgroup divides the order of the group. However the methods are much more complicated, and other harmless-seeming analogs are false.
This classification problem is of interest in other areas, since Hopf algebras occur as invariants of other structures, such as in knot theory, in extensions of von Neumann algebras, and in conformal field theory.
|
Monday, April 19, 1600-1700 |
Speaker : Dag Westerstahl, Filosofiska Institutionen, Goteborgs Universitet.
Title : Logic : Mathematics or Philosophy
?.
Abstract : The question in
the title could refer to (1) the historical fact that logic began within
philosophy but has now partly moved into some mathematics (and computer
science) departments, or (2) the established (but vague) distinction in the
field between philosophical and mathematical logic, or (3) the diverse
attitudes towards logic among mathematicians and philosophers, respectively. None
of these issues is terribly interesting in itself, but they can be helpful in a
brief overview of what logic is today, which is what I will try to give in this
talk.
___________________________________________________________________________________________________________________________________________________________________________________________________
|
Monday, March 8, 1600-1700 |
Speaker : Professor Jouko
Mickelsson, Mathematical Physics, KTH..
Title : Gerbes,
twisted K-theory and quantum fields.
Abstract
: A gerbe is a geometric realisation of integral third cohomology classes in the same way as complex line bundles
may be viewed as geometric objects describing integral second cohomology classes. In this talk I want to explain some
natural constructions in quantum field theory which lead to these geometric
objects.
K-theory describes
properties of families of Fredholm operators
parameterised by some topological space. There is a twisted version of
K-theory, where the twist is a gerbe. Roughly
speaking, one deals with local families of Fredholm
operators related by projective unitary transformations. In the case when the
manifold is a compact Lie group, there are beautiful constructions of the
twisted K-theory classes in terms of a supersymmetric
quantum field theory model which I will explain at the end of the talk.
|
Monday, March 15, 1600-1700 |
Speaker : Peter Jagers, Chalmers.
Title : Fran Malthus och Euler till DNA och polymeraskedjereaktionen.
OBS! Detta ar ett "omatematiskt" foredrag om forgreningsprocesser, som har hallits for en bredare publik. Foredraget ar pa svenska.
Sammanfattning : Individer "lever" och far "barn", som blir de nya individerna. Detta ar det enkla - matematiska - monstret bakom all populationsdynamik, fran fysikens partikelkaskader, via DNA-replikation och cellkinetik upp till djurs, manniskors och aven arters liv och dod. Hur mycket kan ett sadant generellt monster forklara, och hur mycket beror pa den specifika situationen ?
Vad bestammer utdoenderisker ? Hade Malthus ratt i att populationer maste vaxa exponentiellt, om de inte slocknar ut ? Hur kan en snabb tillvaxt av populationer eller en grupp av populationer som helhet, ga hand i hand med ett frekvent utdoende av enskilda "slakter" eller arter ?
|
Monday, March 22, 1600-1700 |
Speaker : Serik Sagitov, Chalmers.
Title : Effective population size and the
coalescent.
Abstract : We start with some basic concepts in population genetics like
random genetic drift, the Wright-Fisher model and effective
population size. Then we introduce the coalescent as a random
genealogical tree for a large Wright-Fisher population. Next we
present some new convergence results toward the coalescent. The time
scales in these limit theorems yield formulae for the
effective size reflecting population age structure and its' mating system.
|
Monday, January 19, 1600-1700 |
Speaker : Rudolf Strasser, Professor i Matematik och larande, Luleå Tekniska Universitet.
Title : Teachers' Mathematics : Special
Maths ?
Abstract
: The
presentation will comment on the widespread assumption that - in university -
future teachers of mathematics need to be taught a (maybe slightly) reduced
form of disciplinary mathematics. Mainly using algebra as a field to illustrate
the arguments, the presentation will offer arguments why future teachers need a
different type of mathematical training in order to prepare for their
professional life. Complementary glimpses into geometry will strengthen the
statements, which also take into account the use of new information technology
in the teaching and learning ("larande") of
mathematics.
|
Monday, January 26, 1600-1700 |
Speaker : Torbjorn Helvik, Matematiske Fag., NTNU Trondheim (Norge).
Title : Cellular automata - not merely a
new kind of science.
Abstract
: When reading
Wolfram's "A New Kind of Science" it is easy to come to the
conclusion that the subject of CA consists of little more than obtaining fancy
patterns using simple programs. The subject is in fact much richer than so.
Cellular automata have been introduced in several different settings, most
notably by von Neumann in the 1960s when studying self-reproducing machines and
by Hedlund and coworkers
around 1970 as endomorphisms of the shift dynamical
system. But different people have studied CA out of different interests and
using different tools - often not knowing about each other. This has led to a
literature which is large but incoherent. In this lecture we present some of
the applicable tools and basic mathematical results on cellular automata. Furthermore,
we talk a little about what is not yet known and what is undecidable
about CA. Finally, we briefly present a new conceptual extension of cellular
automata, which we call higher order CA..
|
Monday, February 2, 1600-1700 |
Speaker : Professor Timothy Gowers,
Title : The Importance of Mathematics.
Abstract
: This is a
video recording of a lecture given by 1998 Fields Medalist
Timothy Gowers at the Clay Millenium
meeting in
|
Monday, February 9, 1600-1700 |
Speaker : Barbara Jaworski, Högskolan i Agder (Norge).
Title : Developing understanding of the
teaching of undergraduate mathematics.
OBS! Note that the
presentation builds on a research study described in the abstract below. Copies
of the article will be available in the lunchroom during the week preceeding the colloquium.
Abstract
: My seminar
will address research into the teaching of mathematics to first year students
at university level in university tutorials. It will make reference directly to
a paper published in ESM Vol. 51 No. 1-2, pp.71-94. Data from observations of
first year university mathematics tutorials were analysed to elicit
characteristics of teaching using a tool, the teaching triad, developed in
earlier research. Analysis explored elements of "sensitivity to
students" and "mathematical challenge" in the observed teaching.
Initial analyses suggested teaching to consist mainly of tutor exposition and
closed questions embodying little challenge for the student. More finely
grained analyses provided insights into pedagogic processes relating teaching
actions, processes and strategies and their learning outcomes, and providing
alternative perspectives on sensitivity and challenge. The research,
distinctively, shows approaches to analysing teaching that start to address
tutor-student interactions related to cognitive construction of mathematics
(here abstract algebra) by undergraduates within the social dimensions of the
tutorial setting. .
|
|
Speakers
: John Tate,
Harvard and (Sir) Michael Atiyah,
Title : The Clay Millenium
problems.
Abstract
: Tate and Atiyah delivered lectures at the Clay Millenium
Conference in May 2000, the same conference that Gowers
spoke at, the video recording of whose lecture we showed at the colloquium on
February 2. The lectures of Tate and Atiyah are
concerned with describing the actual Clay Millenium
problems, and hence are completely independent of Gowers
talk (so it doesn't matter if you missed that one !). There
are seven of these problems, chosen as outstanding open problems at the end of
the 20th century, for the solution of which the Clay Institute created a prize
fund. Tate discusses the first three (two are in number theory, one in
mathematical logic) and Atiyah the last four (which
are in differential geometry/topology and mathematical physics). All the
problems have a long history and a lot of work has already been done on all of
them. Hence these talks are of necessity far more technically sophisticated
than that of Gowers. However, they should still be of
interest to a general mathematical audience.
|
Monday, February 23, 1600-1700 |
Speaker : Georg Lindgren, Matematisk Statistik, Lunds Universitet.
Title : On random waves - even if no two
waves look the same but they satisfy the same statistical law..
Abstract
: Waves on the
sea follow strict physical laws - but it is very difficult to predict the
behaviour of an individual wave even a few seconds ahead. A wave surfer can
learn to spot a good surf wave before it has materialised and use it for a record surf, or avoid it when it's going to be too
dangerous. However, a ship master on a big ship has no chance to steer away
from an oncoming dangerous wave. He has to rely on weather forecasts and on the
statistical laws that predict the probability of hazardous wave conditions
during the expected weather.
To define wavelength and waveperiod is easy for a mathematical wave, but how does
one define it for a constantly changing random sea surface ?
How can one measure wave height when wave crest and wave trough are moving and
all of a sudden disappear ? Is "the seventh
wave" just an allusion to a magic number, or is there any statistical
substance behind it ?
In this talk I shall
describe some of the statistical tools one can use to describe the random
character of sea waves, their height, speed and extension.