Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium


Monday, May 29, 2017

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041



Lecture 1 - 14:15

Cristina Bazgan - Université Paris-Dauphine

Finding community structures in graphs

Abstract:
We investigate the structural and algorithmic properties of community structures and in particular the case with 2 communities. A 2-community structure is a partition of a vertex set into two parts such that for each vertex the numbers of neighbours in/outside its own part and the sizes of the parts are correlated. We show that some well studied graph classes always admit a 2-community structure. Furthermore, a 2-community structure can be found in polynomial time in all these classes, even with additional request of connectivity in both parts. We introduce a concept of a weak 2-community and prove that in general graphs it is NP-complete to find a balanced weak 2-community structure with or without request for connectivity in both parts.

The talk is based on a joint work with Janka Chlebikova and Thomas Pontoizeau.




Lecture 2 - 16:00

Klaus Trümper - University of Dallas at Texas

Wittgenstein's Philosophy and the Discovery Question of Mathematics

Abstract:
Over the span of tens of thousands of years, humans have created an elaborate body of theory unequaled in size and complexity: mathematics. There is a profound philosophical question: Where do all the results of this gigantic body of theory come from? Are they already present in some hidden, possibly metaphysical, location and then discovered by inquisitive minds, or are they created in the same way that engineers design various machines for energy conversion, production of goods, or transportation? Over hundreds of years, this question has been answered in various, often diametrically opposed, ways.

We examine this question using the approach of the philosopher Ludwig Wittgenstein for the resolution of philosophical problems. With the help of modern brain science, we also look into the strange aspect that eminent researchers arrived at and vigorously defended diametrically opposed answers. Indeed, that amazing process is ongoing today.

The talk is based on the book "The Construction of Mathematics: The Human Mind's Greatest Achievement." It assumes no prior knowledge in mathematics or philosophy.



Letzte Aktualisierung: 22.05.2017