An overview of recent research results of our group was given, specifically about our important results on two famous unsolved problems from theory of extension dimension. The lecture received a great deal of attention. It confirmed our leading position in the field of theory of cohomological dimension in which we started conducting research in the 1980's when we successfully solved several open problems on general position of compacta in Euclidean spaces.
B.04 Guest lecture
COBISS.SI-ID: 14295129The purpose was to improve the existing solutions and introduce algorithms for digital control of the tuning fork. This will enable improved precision, faster response, and will reduce the cost of production. In the beginning stage the surface is modelled using cycles in Lie geometry, which enable a compact description. The computation of a step along the surface between cycles will thus be reduced to a simple calculation. In the second stage, the obtained algorithms are extended to more general surfaces using a detailed analysis or the experimentally observed parameters of the tuning fork.
D.01 Chairing over/coordinating (international and national) projects
COBISS.SI-ID: 14487641For the celebrations of the 80th birthday of the founder of the theory of continuous selections of multivalued maps, Ernest Michael (University of Washington, Seattle, USA) and the 50th anniversary of the theory, we were asked by the chief editor Jan van Mill to edit a special issue of the journal Topology and Its Applications (Elsevier North-Holland). In this issue we collected over twenty fundamental works contributed by leading experts in this field from around the world. This is a extremely significant as it positions our group among the world leaders in this field.
C.03 Guest-associated editor
COBISS.SI-ID: 26538752Results of our research are described on possible definite 4-manifolds that a given racional homology sphere Y may bound. The main result is a generalization of Elkies’ Theorem on characterization of the diagonal definite unimodular form in terms of its characteristic vectors to non-unimodular forms. In conjunction with the d-invariant in Heegaard-Floer homology the above mentioned characterization yields a simple method with which one can show that Y cannot bound certain definite forms. The method is especially useful in studying the manifolds that can be bounded by surgeries on knots.
B.04 Guest lecture
COBISS.SI-ID: 13897561"Tenth Prague Topological Symposium " is the longest running topology conference in Europe, organized every 5 years; inviting the leading experts from around the world. Slovenian topologists are present at this conference for the last 15 years, each time with an invited address, which shows the international reputation our group enjoys. We presented the latest developments in the field including the results of our group, specifically the recent constructions of rigid wild Cantor sets with simply connected complements (the existence of such objects was an open problem since 1960’s).
B.04 Guest lecture
COBISS.SI-ID: 14317401For the celebrations of the 80th birthday of the founder of the theory of continuous selections of multivalued maps, Ernest Michael (University of Washington, Seattle, USA) and the 50th anniversary of the theory, we were asked by the chief editor Jan van Mill to edit a special issue of the journal Topology and Its Applications (Elsevier North-Holland). In this issue we collected over twenty fundamental works contributed by leading experts in this field from around the world. This is a extremely significant as it positions our group among the world leaders in this field.
C.03 Guest-associated editor