Quantum walks are considered to be quantum counterparts of classical random walks. With the advancements in quantum information theory, different version of quantum walks and quantum random walks have been developed for application in quantum algorithms and mimicking/simulating dynamics of various physical systems. In this talk I will introduce both, the discrete-time and continuous-time versio...

In this paper we use a natural forcing to construct a left-separated topology on an arbitrary cardinal κ. The resulting left-separated space Xκ is also 0-dimensional T2, hereditarily Lindelöf, and countably tight. Moreover if κ is regular then d(Xκ) = κ, hence κ is not a caliber of Xκ, while all other uncountable regular cardinals are. This implies that some results of [A] and [JSz] are, consis...

The aim of this note is a classification of all nice and all inductively factored reflection arrangements. It turns out that apart from the supersolvable instances only the monomial groups G(r, r, 3) for r > 3 give rise to nice reflection arrangements. As a consequence of this and of the classification of all inductively free reflection arrangements from Hoge and Röhrle (2015) we deduce that th...

Assuming Jensen’s principle ♦, there is a compact Hausdorff space X which is hereditarily Lindelöf, hereditarily separable, and connected, such that no closed subspace of X is both perfect and totally disconnected. The Proper Forcing Axiom implies that there is no such space. The ♦ example also fails to satisfy the CSWP (the complex version of the Stone-Weierstrass Theorem). This space cannot c...

In [23], Todorcevic gives a survey of basis problems in combinatorial set theory, listing nine theorems and six working conjectures — all in the presence of PFA — including the following three of interest to us here: Conjecture 1 (Todorcevic; [23]). If R is a binary relation, then either R ≤ א0 ·ω1 or [ω1]0 ≤ R. Conjecture 2 (Hajnal, Juhasz; [5]). If X is a regular Hausdorff space, then the fol...