LiU / Matematiska Institutionen

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Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

Vi har dessutom ett arkiv av gamla nummer.

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***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v41 2002

Matematiska kollokviet

Onsdagen den 9 oktober, kl. 13.00-14.00 talar Professor Kurt Johansson, KTH

Probability measures from random matrix theory

Sammanfattning: Probability measures coming from random matrix theory, usually from appropriate limits of the spectrum as the size of the matrix goes to infinity, have been the focus of much interest. They occur in spectral problems (quantum chaos), number theory and also unexpectedly in certain probability problems related to random growth and random tilings. I will give some background and then concentrate on the last topics.

Onsdagen den 16 oktober, kl. 13.00-14.00 talar Professor Michael Solomyak, Weizmann Institute of Science, Rehovot, Israel,

On the spectrum of the Laplacian on metric graphs

Sammanfattning: A metric graph is a graph whose edges are viewed as line segments of positive length, rather than just pairs of vertices. The Laplacian on such graph is the operator of second derivative on each edge, complemented by the Kirchhoff matching conditions at vertices. The spectrum of the Laplacian can be quite different, reflecting geometry of a given graph. Recent results on this subject will be reported. The most detailed results concern a special case of graphs, namely the so-called regular trees.

Onsdagen den 23 oktober, kl. 13.00-14.00 talar Dr. Björn Gustafsson, KTH,

Some multiplicative potential theory

Lokal: ISY/MAI:s seminarierum Glashuset, ingång 25.

Välkomna!

Analysseminarium

Fredagen den 11 oktober kl. 13.15-15 talar Anders Björn,

The Perron method for p-harmonic functions

Sammanfattning: The Perron method was introduced by Oskar Perron in 1923 to solve the Dirichlet problem in D, u=f on , where D is a given domain and f a given (boundary value) function. The upper Perron solution is the (pointwise) infimum of superharmonic functions which have boundary values on . Similarly the lower Perron solution is the supremum of subharmonic functions with boundary values . When the upper and lower Perron solutions agree, we say that f is resolutive. In this case the Perron solution is a reasonable solution to the Dirichlet problem, even though it may not take the correct boundary values everywhere. Brelot showed in the 1939 that functions are resolutive.

In this talk we will consider the Dirichlet problem for the non-linear equation

The main result so far has been that every continuous function f is resolutive. In this talk I will discuss some new results including the result that Sobolev functions are resolutive.

In the linear case it is known that if f is perturbed on a set of measure zero, then the Perron solution remains the same. In the non-linear case, I will discuss some new results about perturbation on sets of capacity zero (which are much smaller than general sets of measure zero).

The talk should be accesible to graduate students having some knowledge of Sobolev spaces, e.g. those attending the present graduate course on partial differential equations. It is based on joint work with Nageswari Shanmugalingam, Cincinnati, and Jana Björn.

Lokal: MAI:s seminarierum Beurling

Välkomna!

Vladimir Kozlov

Seminarier i numerisk analys

Professor Per Christian Hansen, Informatics and Mathematical Modelling, Technical University of Denmark, gästar institutionen 14-18 oktober. Han ger två föredrag (båda i seminarierummet Glashuset):

Onsdag 16 okt, kl. 10.15

Inverse Geomagnetic Problems

Monitoring the internal structure and dynamics of vulcanic areas is important. This can be done via solving an inverse problem, in which the underground distribution of magnetic dipole moment is computed from external measurements of the magnetic field anomaly.

In collaboration with Naples University we use a new approach based on multiple levels of data to achieve depth resolution in 3-D potential field models. In this talk we first describe the mathematical model and its discretization, then we discuss the problems associated with obtaining depth resolution, and finally we discuss the use of a new preconditioner for the iterative solution of large-scale problems.

Fredag 18 okt, kl. 10.15

Subspace Preconditioning for Discrete Ill-Posed Problems

We present a two-level iterative method, based on conjugate gradients, for the solution of large-scale discrete ill-posed problems. The algorithm is algebraically equivalent to the two-level Schur algorithm of Hanke and Vogel but involves less work per iteration. The key idea in the algorithm is to project the problem onto a low-dimensional subspace, spanned by "smooth" vectors, which contains a dominating component of the regularized solution. The remaining component is then computed via the Schur complement.

We first review the algorithm and demonstrate how it should be implemented efficiently and reliably, and then we demonstrate its usefulness with numerical examples that give insight into the proper use of the algorithm. Finally we discuss the choice of stopping criteria for the iterations.

Välkomna!
Lars Eldén

Svenska matematikersamfundets höstmöte

Svenska matematikersamfundet kommer att hålla sitt höstmöte vid Linköpings universitet fredagen den 25 oktober, kl 10.30-16.00.

Talare är Professor Bernard Helffer, Université Paris-Sud,

Semiclassical analysis and superconductivity

Professor Robert Seeley, Boston,

Operators of Dirac type in the presence of a conic singular stratum

Docent Nils Dencker, Lund,

The Quest for Solvability

Professor Ira Herbst, Charlottesville,

Dynamics of a particle in a class of long range magnetic fields

Sammanfattningar finns på http://www.matematikersamfundet.org.se

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Välkomna!

Anders Björn

Filmvisning

Torsdagen den 17 oktober, kl. 15.15-16.00 kommer filmen

The CMI Millenium meeting

att visas. Filmen är c:a 30 minuter.

Den kommer att följas av ytterligare tre filmer från det mötet torsdagarna 31 oktober, 14 och 28 november, kl. 15.15-16.30, med föredrag av Atiyah, Gowers och Tate.

Filmerna finns på VHS-NTSC kasetter och kan lånas av den som så önskar efter respektive filmvisning.

Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.

Välkomna!

Anders Björn och Lars Eldén

Övrigt

Sommarinstitutet 2003 - learning partners building identy

Rådet för högskoleutbildning inbjuder till ett Sommarinstitut för unga universitetslärare och doktorander. Syftet är bl a att öka entuiasmen och intresset för lärande och undervisning.

Ansökan skickas senast den 15 oktober till nästa års institut som äger rum den 18-23 maj. Vidare information:

www.hgur.se/sommarinstitutet/index

Inbjudan finns på anslagstavlan i postrummet.

Resestipendier ur Nils-Eric Svenssons fond

Stiftelsen Riksbankens Jubileumsfond utlyser två resestipendier om vardera cirka 100.000 kr för att ge möjlighet för yngre disputerade svenska forskare inom Riksbanksfondens verksamhetsområde att resa till, och under kortare tid vistas, i en framstående europeisk forskningsmiljö.

Ansökan sändes till Riksbankens Jubileumsfond, senast torsdag den 9 januari 2003.

Närmare upplysningar: margareta.buler@rj.se

Inbjudan finns på anslagstavlan i postrummet.



Mer information om MAI finns på under MAIs hemsida
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-149403, Email: litemat@mai.liu.se

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Senast ändrad: Wed 2012-08-29; 15:43 CEST