Dieses zweitägige DMV-Studierendenkolleg beschäftigte sich mit dem Thema Unabhängigkeit. In mehreren Vorträgen und Workshops erhielten die Teilnehmenden eine Einführung in und einen Überblick über das Thema sowie seine Berührungspunkte mit anderen Teilen der Mathematik, hier exemplarisch unendliche Kombinatorik. Final wendeten sich die Forschungsvorträge dem aktuellen Stand der Wissenschaft zu.

Weitere Informationen: www.math.uni-hamburg.de/projekte/undecidability/

The FOMUS workshop was held at the Center for Interdisciplinary Research of Bielefeld University from the 18th to the 23rd of July. Within this framework approximately 80 graduate students, junior researchers and leading experts gathered in order to investigate and discuss suitable foundations for mathematics and their qualifying criteria, with an emphasis on HoTT/Univalent Foundations and set theory. This interdisciplinary workshop, designed as a hybrid between summer school and research conference, was aimed at students and researchers from the fields of mathematics, philosophy and computer science.

Zermelo-Fraenkel axioms are widely assumed to be the foundation of mathematics within the mathematical practice of set theory. However, an increasing number of researchers are currently working on the Univalent Foundations as an alternative foundation of mathematics. This relatively young approach is based on Homotopy Type Theory, which is a link between Martin Löf's intuitionistic type theory and the homotopy theory from topology.

The workshop was opened with an introduction to these two different foundational theories, with an emphasis on the less popular homotopy type theory, and then progressed into indepth panel discussions and (research) talks. With regard to the philosophical discipline of mathematics, the formal requirements of the foundations of mathematics, their limitations and their naturality were examined. Recently, it has become increasingly important to formalise mathematics by computer-aided formal proof systems, such as Coq. With this in mind, it was investigated which foundation is most suitable for the changing needs of mathematical practice.

Weitere Informationen: fomus.weebly.com/
Abstracts und Videos der Vorträge: fomus.weebly.com/talks-abstracts--videos.html

"Unfehlbarkeit durch Formalismus? – Ein interdisziplinärer Blick auf Möglichkeiten, Grenzen und Folgen einer methodischen Revolution der Mathematik." - Unter diesem Titel kamen ca. 80 Studierende und zehn Dozenten verschiedener Fachrichtungen zusammen, um über formale Mathematik nachzudenken. Die Zukunft dieser in den letzten Jahren immer erfolgreicheren Form, Mathematik zu betreiben, wirft Fragen zu den Grundlagen der Mathematik, zu algorithmischen Problemen im Bereich des automatischen Beweisens, zu wissenschaftstheoretischen Themen, sowie zu soziologischen Aspekten der mathematischen Forschung auf. Dementsprechend waren Dozierende und Teilnehmende aus den Bereichen der Mathematik, Informatik, Philosophie und Soziologie, sowie angrenzender Fachbereiche beteiligt.

Weitere Informationen: formale-mathematik.weebly.com

Recently science and industry deals with growing amount of data, often of high dimensionality, termed "big data", coming for example from experiments in biology or computer vision.
The easiest example of a topological approach to data is clustering, where one groups together data points according to a loose notion of proximity. This corresponds to computing the zeroth homology of a geometric object interpolating the data points.

Persistence is the philosophy of not choosing just one geometric object to model the data, but a whole family, parameterized by how close two data points have to be, to be considered topologically close in the geometric model. Technically, one defines a simplicial complex by connecting points which are close enough.

Weitere Informationen: www.konradvoelkel.com/homepage/events/topology-and-big-data/