Member of the project group dr. Zdomskyy gave an invited one-hour plenary talk at the international meeting Set Theory in Oberwolfach in which he presented some of our new results, which reveal the heretofore unknown topological nature of classical combinatorial properties of filters which have been intensively studied in recent decades.
B.04 Guest lecture
COBISS.SI-ID: 16980825Member of the project group, postdoc dr. Virk presented an invited talk, describing some of the latest results of our research, at the international meeting Workshop Large Scale Dimensions, Regensburg, July 25-29, 2016.
B.04 Guest lecture
COBISS.SI-ID: 17731673Doctoral student in our project group Govc presented an invited talk, describing his doctoral thesis results, at the international meeting Oporto Meeting on Geometry, Topology and Physics (21 ; 2015 ; Lisbon).
B.03 Paper at an international scientific conference
COBISS.SI-ID: 17231705Leader of the project group dr. Repovš presented an invited 90-minutes opening plenary talk, describing some of the latest results of our research, at the international meeting Glances @ Manifolds, low-&-high-dimensional (2015 ; Jagiellonian University, Kraków).
B.04 Guest lecture
COBISS.SI-ID: 17374553Thesis of our doctoral student Lampret investigates qualitative and quantitative properties of homology tables associated to standard objects from algebra and topology. In the first chapter, he formulates and proves Sköldberg's theorem of algebraic Morse theory. In the second, as the first steps he looks at examples of how AMT works on simplicial complexes. In the third, he applies AMT on the bar resolution for exterior algebras, which produces a new minimal resolution. With it, he computes the Hochschild homology over fields and over \mathbb{Z}, as well as determines the multiplicative structure of cohomology. In the fourth chapter, he constructs a family of matchings for the solvable family of Lie algebras of triangular matrices w.r.t. any partial order, which drastically reduce the chain complex. In the case of a linear ordering (i.e. triangular matrices), these matchings enable a thorough study of Chevalley homology (free part, first occurences of primes in the torsion, low and high degrees, homological dimension). In the case of orderings of height 1 or 2, they allow direct computations of the cohomology algebras.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 17762649