Arbeitsgruppe Diskrete Mathematik
Angewandte Geometrie und Diskrete Mathematik
Auf dieser Seite werden die Termine der Arbeitsgruppe Diskrete Mathematik verwaltet.
|Seminar:||MI 02.06.020, Di, 10:30-12:00|
VorträgeVorträge des Oberseminars sind mit OS gekennzeichnet, die des Doktorandemseminars mit DS.
|Vortrag||Di 23.11.||Oliver Cooley / Andreas Würfl||Latin Square Games / Blow-up Lemma Introduction||10:30 Uhr, MI 02.04.011|
|Vortrag||Di 7.12.||Anusch Taraz / Peter Heinig||Hamiltonicity in random planar graphs / Torsion in the integral homology of (random) simplicial complexes||11:30-13:00, MI 02.06.020|
|Vortrag||Di 14.12.||Beata Faller||Combinatorial and probabilistic methods in biodiversity theory (abstract)||10:30-12:00, MI 02.06.020|
|Vortrag||Di 21.12.||Kosta Panagiotou||Percolation in Random Networks (abstract)||10:30-12:00, MI 02.06.020|
|Vortrag||Di 11.1.||Carl Georg Heise||Colouring regular hypergraphs||10:30-12:00, MI 02.06.020|
|Vortrag||Fr 21.1.||Alex Scott||Triangles in random graphs (abstract)||14:15-15:45, MI 03.06.011|
|Vortrag||Di 25.1.||Martin Aigner / Emo Welzl (Fakultätskolloquium)||Von Irrationalzahlen bis perfekte Matchings: Markovs Jahrhundertvermutung / tba||16:00-18:30, MI HS3|
|Vortrag||Di 1.2.||Maximilian Schlund||Dreieckszerlegungen dichter Graphen (abstract)||10:30-12:00, MI 02.06.020|
|Vortrag||Di 8.2.||Anusch Taraz||Random Planar Graph Processes||10:30-12:00, MI 02.06.020|
Combinatorial and probabilistic methods in biodiversity theory:A central question in conservation biology is how to predict and maximize biodiversity as species face extinction. There are numerous ways to measure the biodiversity of a group of species, and one which recognizes the evolutionary linkages between species is phylogenetic diversity (PD). Briefly, given a subset of taxa, the phylogenetic diversity of that subset is the sum of the evolutionary distances of the edges of the minimal phylogenetic tree that connects this subset.
In the last three years, the aim of my research has been to develop and study models that are based on PD and can be used to forecast or optimize future biodiversity. This talk gives an overview of our models and findings. We discuss the computational complexity of optimization problems that aim to find species sets with maximum PD in different scenarios, and examine random extinction models under various assumptions to predict the PD of species that will still be present in the future.
Percolation in Random NetworksIn the classical Erdös-Rényi model of random graphs we begin with an empty graph on n vertices, and in each round we add an edge, drawn uniformly at random from the set of all possible edges. A celebrated result states that if we parametrize n/2 rounds as a single time step, a phase transition occurs at time 1. There, a giant connected component that contains a linear in n number of vertices makes its emergence for the first time.
An important question in this context is whether the appearance of the giant can be delayed or accelerated by modifying the process slightly. One such modification is motivated by the power of choice: in each round we add an edge, which can be chosen according to some desired rule between two (or more) random edges.
In this talk I will review some results regarding such processes. Then I will show how the precise study of them can be reduced to finding solutions of certain partial differential equations, and I will reveal a connection to singularity analysis of generating functions. The talk will conclude with future perspectives and some conjectures.