Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Bodil Stavklint email@example.com senast torsdagar kl 08.00.
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Ett informationsblad från matematiska institutionen vid Linköpings universitet
Onsdagen den 27 oktober, kl. 13.00-14.00 talar Professor Anders Björner, KTH, angående:
Blockers and vanishing ideals of subspace arrangements.
Sammanfattning: The blocker of a set family is the collection of inclusionwise minimal sets that intersect all sets in . This construction is well-known in combinatorics and combinatorial optimization. The corresponding construction on set partitions (and more generally on geometric lattices) arises in the study of vanishing ideals of arrangements of linear subspaces in a vector space.
I will survey examples and properties of blockers and a combinatorial duality that they satisfy, beginning with some new results on blocker duality in general posets. I will then describe the relevance of this concept for vanishing ideals that are generated by products of linear forms. The results also touch on some Turan-type problems from extremal combinatorics.
The talk is based on joint work with A. Hultman, I. Peeva and J. Sidman.
Onsdagen den 3 november, kl. 13.00-14.00 talar Professor Martina Šimunková, Liberec, Czech Republic angående:
The Poisson Integral and the Kelvin Transform
Sammanfattning: The Poisson integral which gives an explicit solution of the Dirichlet problem of the Laplace equation on a ball plays an important role in classical potential theory. There are several possibilities to derive the Poisson integral - some of them are based on the Kelvin transform. The connection between the Poisson integral and the Kelvin transform will be shown. Also Kelvin type transforms of elliptical operators will be described.
Lokal: ISY/MAI:s seminarierum Glashuset, ing 25.
Svante Linusson och
Onsdagen den 27 oktober, kl 16:00 - ca 17 talar Rainer Brüggemann, matematiker från Leibniz - Institute of Freshwater Ecology and Inland Fisheries, Berlin angående:
Rankings by Partial Orders.
Abstract: The discussion about risk assessment of chemicals was renewed by the appearance of the so-called White book of the EU and by the publication of REACH. In context with this development the need of a priority setting - procedure becomes enhanced relevance: A ranking procedure is needed to select the most important chemicals for a refined analysis by e.g. the mathematical model package EUSES. If chemicals are to be ranked with respect to their hazard potential one is faced with typical problems of multicriterial evaluation: There are several indicators by which a ranking could be performed. How can we get a unique decision, and how we can avoid subjective decisions and maintain a maximum of transparency within the evaluation procedure?
In my talk very simple elements of the theory of partially ordered sets are applied on the multicriterial decision problem, typical questions, like
Examples are taken from chemistry, biology and water management.
Lokal: Kompakta rummet
Olle Eriksson och Anders Grimvall
Fredagen den 22 oktober kl. 15.15-17.00 presenterar Professor Juan Manfredi, University of Pittsburgh, sitt ''virtuella laboratorium för teknik och matematik'' och talar speciellt om sina erfarenheter av linjär algebra-undervisning.
Gunnar Aronsson, Bengt Ove Turesson
Onsdagen den 27 oktober kl 10.15 försvarar Jonna Gill sin licentiatavhandling med titeln
The -assignment Polytope and the Space of Evolutionary Trees.
Opponent är professor Anders Björner från KTH.
Abstract: This thesis consists of two papers. The first paper is a study of the structure of the -assignment polytope, whose vertices are the -matrices with exactly :s and at most one in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised.
Two equivalent representations of the faces are given, one as -matrices and one as ear decompositions of bipartite graphs. These tools are used to describe properties of the polytope, especially a complete description of the cover relation in the face lattice of the polytope and an exact expression for the diameter.
The second paper studies the edge-product space for trees on . This space is generated by the set of edge-weighted finite trees on , and arises by multiplying the weights of edges on paths in trees. These spaces are closely connected to tree-indexed Markov processes in molecular evolutionary biology. It is known that has a natural -complex structure, and a combinatorial description of the associated face poset exists which is a poset of -forests.
In this paper it is shown that the edge-product space is a regular cell complex. One important part in showing that is to conclude that all intervals , , have recursive coatom orderings.
Wednesday 27 October 15.15-16
Seminar series on stochastic iterations continues. Theme: Contraction conditions and formulation of limit theorems.
NONLINEAR OPTIMIZATION, EQUATIONS AND LEAST SQUARES - a course for graduate students´.
This course has been approved by LiTH FoFu-nämnden as "Fakultetsgemensamma forskarutbildningskursen". It will start on Wednesday, week 3, and will take about 16-17 weeks (one seminar per week). The course is worth 6 points.
Students will get acquaintance with the most effective numerical methods in nonlinear optimization, equations and least squares, many of which have been developed only in recent years. They will be involved in presenting the material. The basic book:
Jorge Nocedal and Stephen J. Wright "Numerical Optimization", Springer, 1999
For more information about the book see: http://www.ece.nwu.edu/~nocedal/book/num-opt.html
Students background: basic calculus, numerical linear algebra and optimization. Any gap in the background can be closed by students at the beginning of the course by intensive self-study with a help of the lecturer.
Mer information om MAI finns på MAIs hemsida.
Material till Lite Mat lämnas till Bodil Stavklint senast torsdagar kl 08.00.
Linköpings universitet, 581 83 Linköping
Tel 013-281000, Fax 013-149403
Sidan underhålls av: LiteMat
Senast ändrad: Wed 2012-08-29; 15:43 CEST