University
of Jyväskylä
Mathematics
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Main research and development areas
The research at the Department of Mathematics has been concentrated
primarily on mathematical analysis. The main research topics are: conformal
geometry, non-linear potential theory and partial differential equations,
and geometric measure theory. The groups are in a close cooperation with
each other. The research is by its nature mathematical basic research. The
research groups in Jyväskylä have very close connections to the researchers
in the Department of Mathematics of University of Helsinki, and broad and
active international contacts.
New directions of research emphasis at the Department include stochastics
and the mathematical theory of computation. Both of these connect also to
the increasingly active application area of computationally intensive
mathematical modeling. For the purpose of coordinating this type of work
within the University, a new research unit, the Center for
Mathematical
and Computational Modeling (CMCM) has recently been established. This unit
brings together researchers from the Departments of Mathematics,
Statistics, and Mathematical Information Technology, and from several
research groups in the natural sciences.
Researchs highlights in last years
The joint research program of Jyväskylä and Helsinki in geometric analysis
was evaluated with the grade excellent plus in the international evaluation
carried out in 1998 by the Academy of Finland. It was considered to be the
best research program in mathematics and computer science in that
evaluation. The leaders of the research groups mentioned above are K.
Astala, T. Kilpeläinen, and P. Mattila. The groups have achieved
significant international position. Astala received in 1995 the
distinguished Raphaël Salem prize in analysis as a recognition of his
research, and Astala and Mattila were invited lecturers in ICM-98, the
international congress of mathematicians in 1998. The Ph.D. thesis of Petri
Huovinen of 1997 was evaluated the best in mathematics in Finland in that
year.
Research Programmes of Academy of Finland
Nonlinear mathematical and computational methods in elasticity, composites
and PDE's
(prof. Kari Astala)
Geometrinen analyysi (prof. Kari Astala)
Konforminen geometria ja analyysi monistoilla (prof. Kari Astala, JY ja
HY)
Fraktaalityyppisten joukkojen ja mittojen geometria (nuor. tutkija Maarit
Järvenpää)
Potential theory and nonlinear partial differential equations (vanh.
tutkija, dos. Tero Kilpeläinen)
Konforminen analyysi (prof. Pekka Koskela)
Geometrinen mittateoria (prof. Pertti Mattila)
Homogenisaatio ja sen sovellutukset materiaalitieteissä
hemivariaatioepäyhtälöt (nuor. tutkija Markku Miettinen)
Hajautettu rinnakkaislaskenta (prof. Pekka Orponen)
Complex systems and their
interdisciplinary application in
science
(consortium master proposal)
(prof. Pekka Orponen)
Kleinin ryhmät ja deformaatioavaruudet (tutkijatohtori Jouni Parkkonen)
A Selection of Publications
K. Astala: Area distortion of quasiconformal mappings, Acta Math. 173
(1994), 37-60.
K. Astala and M. Miettinen: On quasiconformal mappings and 2-dimensional
G-closure problems, Arch. Rational Mech. Anal. 143 (1998), 207-240.
J. Heinonen, T. Kilpeläinen and O. Martio: Nonlinear Potential Theory of
Degenerate Elliptic Equations, Oxford University Press, 1993.
J. Heinonen and P. Koskela: On quasiconformal maps in metric spaces with
controlled geometry, Acta Math. 181 (1998), 1-61.
T. Kilpeläinen and J. Mal´y: The Wiener test and potential estimates for
quasilinear elliptic equations, Acta Math. 172 (1994), 137-161.
W. Maass, P. Orponen: On the effect of analog noise in discrete-time
analog computations. Neural Computation 10 (1998), 1071-1095.
P. Mattila: Geometry of Sets and Measures in Euclidean Spaces, Cambridge
University Press, 1995.
P. Mattila, M.S. Melnikov and J. Verdera: The Cauchy integral, analytic
capacity, and uniform rectifiability, Ann. of Math. 144 (1996), 127-136.
P. Orponen, K. Ko, U. Schöning, O. Watanabe: Instance complexity.
Journal of the Association for Computing Machinery 41 (1994), 96-121.
Graduate schools
Graduate School in Mathematical Analysis and Logic
Graduate School in Computing and Mathematical
Sciences
Graduate School in
Mathematics, Physics and Chemistry Education
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