This was an invited plenary talk at the European Mathematical Congress in Krakow, at the Special Session devoted to Geometric Topology. The key results of this program group in geometric topology were presented.
B.04 Guest lecture
COBISS.SI-ID: 16328025This was an invited plenary talk at the 7th European Conference on Elliptic and Parabolic Problems, Gaeta (Italy). The key results of this program group in nonlinear analysis were presented.
B.04 Guest lecture
COBISS.SI-ID: 16299609This was an invited plenary talk at the Eighth Italian-Spanish Conference on General Topology and its Applications, Università degli Studi di Trieste, Trieste, Italy. The key results of this program group in topological groups were presented.
B.04 Guest lecture
COBISS.SI-ID: 16387929This was a colloquium at the Brigham Young University in Provo, USA. The key results of this program group in geometric group theory were presented.
B.05 Guest lecturer at an institute/university
COBISS.SI-ID: 16431193The notion of topological complexity was introduced by M. Farber in 2001 as a measure of discontinuity of motion planning algorithms on a configuration space of a robot. Some seven years later N. Iwase and M. Sakai presented the notion of monoidal topological complexity that they have shown to be a special case of the fibrewise pointed Lusternik-Schnirelmann category. Hence, numerous methods that work for the LS category can be reused in this fibrewise setting in order to obtain the analoguous results for the monoidal topological complexity. We derive an upper bound for the topological complexity of a mapping telescope almost directly from the fibrewise definition. With a bit more effort we find two alternative fibrewise definitions of monoidal topological complexity, which are analogous to the Whitehead and Ganea definitions of the LS category. From a fibrewise diagram connecting the two definitions we obtain several lower bounds, in particular the stable and the weak topological complexity. We compare these lower bounds to one another and consider some cases where equalities occur.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 263847936