Agnieszka Widz
Agnieszka Widz: Random graph
05/03/24 07:47
Tuesday, March 5, 2024 17:15
Location: A.4.1 C-19
Speaker: Agnieszka Widz
Title: Random graph
Abstract: The Random Graph can be generated almost surely by connecting vertices with a fixed probability \(p\in(0,1)\), independently of other pairs. In my talk, I will recall the construction and explore interesting properties of the Random Graph, investigating the impact of varying probabilities for each edge. Specifically, I will characterize sequences \((p_n)_{n\in\mathbb{N}}\) for which there exists a bijection \(f\) between pairs of vertices in \(\mathbb{N}\), such that if we connect vertices \(v\) and \(w\) with probability \(p_{f(\{v,w\})}\), the Random Graph emerges almost surely.
Location: A.4.1 C-19
Speaker: Agnieszka Widz
Title: Random graph
Abstract: The Random Graph can be generated almost surely by connecting vertices with a fixed probability \(p\in(0,1)\), independently of other pairs. In my talk, I will recall the construction and explore interesting properties of the Random Graph, investigating the impact of varying probabilities for each edge. Specifically, I will characterize sequences \((p_n)_{n\in\mathbb{N}}\) for which there exists a bijection \(f\) between pairs of vertices in \(\mathbb{N}\), such that if we connect vertices \(v\) and \(w\) with probability \(p_{f(\{v,w\})}\), the Random Graph emerges almost surely.
Agnieszka Widz: Almost disjoint magic sets
27/02/22 11:07
Tuesday, March 1, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Agnieszka Widz
Title: Almost disjoint magic sets
Abstract: Given a family of real functions F we say that a set M ⊆ ℝ is magic for F if for all f, g ∈ F we have f [M ] ⊆ g[M ] ⇒ f = g. This notion was introduced by Diamond, Pomerance and Rubel in 1981. Recently some results about magic sets were proved by Halbeisen, Lischka and Schumacher. Inspired by their work I constructed two families of magic sets one of them being almost disjoint and the other one being independent. During my talk I will sketch the background and present the proof for the almost disjoint family, which uses a Kurepa tree.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Agnieszka Widz
Title: Almost disjoint magic sets
Abstract: Given a family of real functions F we say that a set M ⊆ ℝ is magic for F if for all f, g ∈ F we have f [M ] ⊆ g[M ] ⇒ f = g. This notion was introduced by Diamond, Pomerance and Rubel in 1981. Recently some results about magic sets were proved by Halbeisen, Lischka and Schumacher. Inspired by their work I constructed two families of magic sets one of them being almost disjoint and the other one being independent. During my talk I will sketch the background and present the proof for the almost disjoint family, which uses a Kurepa tree.