The plenary talk given at the International conference on nonlinear operators, differential equations and applications, July 5-8, 2011 (Cluj-Napoca, Romunija) presented the state of the art of the research in the analysis of some phenomena governing the behaviour of non-Newtonian fluids. The exhaustive mathematical description given in this talk is in accordance with the results obtained in experiments. Other plenary talks have been given by renowned mathematicians from Chicago and Princeton Universities, Scuola Normale Superiore Pisa, EPFL Lausanne, Tübingen or Nara(Japan). The interest given to this talk confirmed the leading position in this field, which lies at the interface between pure and applied nonlinear analysis.
B.04 Guest lecture
COBISS.SI-ID: 15999833Member of our research group was the doctoral thesis advisor of D. Franetič. Short summary of the thesis: The relationship between ▫$\lor$▫-decompositions of a coH-space ▫$C$▫ and decompositions of the identity as a sum of pairwise orthogonal idempotents in the image of the representation ▫$[C,C] \to \text{End}(H_\ast(G))$▫ is studied. We show that the image of this representation is a semiperfect ring for every finite $p$-local coH-space ▫$C$▫, which implies a strong form of Wilkerson's theorem. The discussion is based on the description of the algebraic structure ▫$[C,C]$▫, which is called a loop near-ring. Local loop near-rings are introduced, and a theorem of unique ▫$\lor$▫-decompositions of coH-spaces, which is completely analogous to the Krull-Schidt-Azumaya theorem for modules, is proven. Dual results hold for H-spaces.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 16196441Program leader presented in one-hour lecture at the central research institute for mathematics in Romania the results of our group, giving an overview of the latest developments in the field including the results of our group, specifically the constructions of rigid wild Cantor sets with simply connected complements (the existence of such objects was an open problem since the 1950’s). The talk received a great deal of interest among the present specialists in the field. Our results came as a surprise since we have constructed completely new types of wild Cantor sets. This was an important promotion of Slovenian science.
B.05 Guest lecturer at an institute/university
COBISS.SI-ID: 15867737