This was an invited talk at the international conference Spring Topology and Dynamics Conference, March 23-25, 2013, Central Connecticut State University, New Britain, CT, USA. The results were presented from the paper Dikranjan, Dikran N.,Dense subgroups of compact abelian groups.
B.04 Guest lecture
COBISS.SI-ID: 16825945This was an invited plenary talk by Banakh at the international conference Topology and Its Applications, Nipissing University in North Bay, Ontario, Canada, July 23-26, 2013. New results of this project group in geometric topology were presented, related to some long standing open problems and conjectures, in particular on fixed fractals of multi-valued maps.
B.04 Guest lecture
COBISS.SI-ID: 16831577An important problem with sensor networks is that they do not provide information about the regions that are not covered by their sensors. If the sensors in a network are static, then the Alexander Duality Theorem from classic algebraic topology is sufficient to determine the coverage of a network. However, in many networks the nodes change position with time. In the case of dynamic sensor networks, we consider the covered and uncovered regions as parametrized spaces with respect to time. Parametrized homology is a variant of zigzag persistent homology that measures how the homology of the levelsets of the space changes as we vary the parameter. We present a few theorems that extend different versions of classical Alexander Duality theorem to the setting of parametrized homology theories. This approach sheds light on the practical problem of 'wandering' loss of coverage within dynamic sensor networks.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 16756057