FB 6 Mathematik/Informatik

Institut für Mathematik

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WS 2019/20

06.11.2019 um 17:15 Uhr in 69/125

Prof. Dr. Takayuki Hibi (Osaka University)

Reflexive Polytopes

13.11.2019 um 17:15 Uhr in 69/125

Prof. Dr. Annette Huber-Klawitter (Albert-Ludwigs-Universität Freiburg)

News on Period Numbers

Period numbers are complex numbers obtained by integrating a differential form with rational coefficients over a suitable domain of integration, also defined over the algebraic numbers. They are obiquitous in mathematics. Examples are π, log(2), ζ(3). Their transcendence properties are the object of long-standing conjectures. We report on joint work with Wüstholz, finally settling the case of 1-forms.

20.11.2019 um 17:15 Uhr in 69/125

Dr. Liam Solus (KTH Royal Institute of Technology, Sweden, & MPI Leipzig)

Probability, Combinatorics, and Causality

Causality, the field of mathematical statistics aimed at quantifying causal relationships based on data, is rapidly growing due to its connections and applications to the modern fields of artificial intelligence and machine learning. Causal models are intuitively represented using graphs with directed edges, and consequently the modern theory of causality finds its roots in a marriage between probability and combinatorics: namely, the study of probabilistic graphical models. As a result, many of the data-driven approaches to learning a causal model rely fundamentally on the combinatorics of directed graphs. Recently, modern combinatorics, and its relationship with graph theory, has opened doors that allow for ideas from discrete geometry and algebra to come to bear on this problem of "causal model discovery". In this talk, we will take a tour through these new developments beginning at their roots: we will start with a discussion of probabilistic graphical models and their refinement to causal models, we will see some connections to discrete geometry, and then we will analyze the resulting data-driven learning algorithms for addressing the problem of causal model discovery. Along the way, we will stop and see some resulting combinatorial problems and avenues for future work.

27.11.2019 um 17:15 Uhr in 69/125

Prof. Dr. Max Horn (Universität Siegen)

On the construction and classification of ‘small’ groups

In this talk, we will review how each finite group can be disassembled into a unique set of "simple" groups, similar to the unique prime factorization of natural numbers. This raises various questions; for example: which simple pieces are there? And: in which ways can one glue these pieces together to form new finite groups? The main focus of this talk will be on this last question, and we will discuss it in the context of classifying (almost) all groups of order at most 20,000.

04.12.2019 um 17:15 Uhr in 69/125

Prof. Dr. Matthew Kahle (The Ohio State University)

Random 2-dimensional simplicial complexes

We will survey the emerging field of stochastic topology, especially from a combinatorial point of view. In particular, we will discuss a number of results by various people for the 2-dimensional random simplicial complex introduced by Linial and Meshulam in 2006. We will pay particularly attention to thresholds for various topological properties, and the notion of a "phase transition". We will also point out some open problems and promising directions for future work. This talk is intended for a broad mathematical audience, and will largely be self contained.

11.12.2019 um 16:15 Uhr (!) in 69/125

Prof. Dr. Heidemarie Bräsel (Otto-von-Guericke-Universität Magdeburg)

Ethnomathematik  – Geometrie auf drei Kontinenten

08.01.2020 um 17:15 Uhr in 69/125

Jun.-Prof. Dr. Lena Wessel (Pädagogische Hochschule Freiburg)

Professionsorientierte Fachwissenschaft am Beispiel abstrakter Algebra im Sekundarstufenlehramt

Am Standort Freiburg werden im Kooperationsnetzwerk FACE (Freiburg Advanced Center of Education – School of Education) im Handlungsfeld Lehre Ansätze zur „Professionsorientierten Fachwissenschaft im Lehramt“ fächerübergreifend entwickelt und erprobt. Für Mathematik-Studierende der Pädagogischen Hochschule im Lehramt Sekundarstufe wurde in mehreren Zykeln ein Veranstaltungskonzept für den Lerngegenstand abstrakter Algebra entwickelt und erprobt. Im Vortrag werden zentrale Design Prinzipien des Veranstaltungskonzepts theoretisch fundiert und ihre Umsetzung exemplarisch dargestellt. Darüber hinaus werden aus der Begleitbeforschung zum Permutationsbegriff gewonnene Einsichten zu Herausforderungen und Bedingungen diskutiert und unter Einbezug von Studierendenevaluationen Konsequenzen für die Weiterentwicklung des Veranstaltungsformats gezogen.

15.01.2020 um 17:15 Uhr in 69/125

Prof. Dr. Christiane Benz (Pädagogische Hochschule Karlsruhe)

Den Blick schärfen – Strukturierende Wahrnehmung als Grundlage für zentrale mathematische Prozesse und Kompetenzen

22.01.2020 um 17:15 Uhr in 69/125

Dr. Georg Tamme (Universität Regensburg)

Descent in algebraic K-theory

29.01.2020 um 17:15 Uhr in 69/125

Prof. Dr. Monika Ludwig (TU Wien)

Geometric Valuation Theory