Conferences by BIRS in Canada are prestigous meetings of researchers working in very active areas of mathematics and it is a special honour to lecture in front of this audience. We presented new results concerning intersection forms of 4-manifolds bounded by special 3-manifolds obtained as surgeries on a knot. The results are important in invariants of 3-manifolds and form a basis for defining concordance invariant of knots in the framework of Heegaard-Floer theory.
B.03 Paper at an international scientific conference
COBISS.SI-ID: 15172697Our research group has received attention for its results, which is also wittnessed by invitations from abroad. In 2009 dr. Cencelj was invited by the Brigham Young University, Provo, which is one of the leading centers of geometric topology in U.S., for a three week visit. The title of the talk was Combinatorial Approach to Coarse Geometry. The lecture received great attention and it confirmed our role in geometric topology and coarse geometry.
B.04 Guest lecture
COBISS.SI-ID: 15179609Dr. Dikranian was Guest Editor of the Special issue of the respected international SCI journal Topology and Its Applications, published by the well known Dutch publishers Elsevier North Holland, dedicated to the memory of the celebrated Czech topologist Jan Pelant (1950-2005).
C.03 Guest-associated editor
COBISS.SI-ID: 26538752One of the basic problems of homotopy theory is the realization of groups in terms of homotopy invariants, i.e., the question, which groups can be realized as a homotopy invariants of topological spaces with certain properties. In this setting the problem of realization of countable groups as fundamental groups of compacta is the most interesting and it was open for twenty years. At the conference the author presented a proof of the realization theorem which answers this question in affirmative.
B.03 Paper at an international scientific conference
COBISS.SI-ID: 15535705The doctoral dissertation contains a definition of descending and ascending regions of critical cells of a discrete Morse function. A consistency result for the obtained objects is given: as in the case of smooth Morse functions, a decomposition of the domain into nonintersection regions which are, after possibly finitely many subdivisions and extensions of the underlying discrete vector field, topological discs. A construction based on the discrete vector field is also described. This leads to an algorithm which is applied to qualitative analysis of natural and artificial data sets.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 15185241