Mathematics Department Colloquium : Spring 2004 schedule


   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, Cambridge University (Video Recording).

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 Paris, May 2000. Gowers' lecture is not about the Clay Millenium Prize Problems themselves (there are further lectures about these which we can show if there is sufficient interest), rather it takes the form of a general argument for the important place which mathematics does and should continue to occupy in our culture. His remarks appear to be partly directed toward the French Finance Minister, who is sitting in the audience! But it includes some actual mathematics, at a level accessible to a very wide audience, including undergraduates (it is mostly combinatorics, combinatorial geometry and number theory).


   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. .


   Monday, February 16, 1545-1730 (NOTE THE UNUSUAL TIME !!)

Speakers : John Tate, Harvard and (Sir) Michael Atiyah, Cambridge (video recordings).

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.