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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
Organisation: Andreas Würfl

Konkrete Vortragstermine können von diesen Zeiten abweichen.


Vorträge des Oberseminars sind mit OS gekennzeichnet, die des Doktorandemseminars mit DS.

Datum Vortragende(r) Thema Zeit/Raum
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 Networks

In 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.

Triangles in random graphs

Abstract: Let X be the number of triangles in a random graph G(n,1/2). Loebl, Matousek and Pangrac showed that X is close to uniformly distributed modulo q when q=O(log n) is prime. We extend this result considerably, and discuss further implications of our methods for the distribution of the number of triangles in G(n,p). This is joint work with Atsushi Tateno (Oxford).

Dreieckszerlegungen dichter Graphen

Abstract: Ich werde etwas zu den Beweisen und der Beweistechnik von Chetwynd,Häggkvist und Gustavsson erzählen (Beziehung von Dreieckszerleungen und lateinischen Quadraten, dünnbesetzte teilweise gefüllte Quadrate und die Verallgemeinerung auf K_k-Zerlegungen) am Ende werde ich noch auf unsere Experimente mit zufälligen lateinischen Quadraten und die dabei auftretenden Schwellenwertphänomene eingehen.

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.