This seminar series focuses on topics at the interface of geometry, topology, and their applications.
Throughout the semester, the programme follows several main thematic strands that highlight different perspectives on topology and geometry and their role in the sciences:
Entanglement arises in various materials, such as textiles, DNA strands, molecular weavings, etc. This module explores how topological invariants, obtained from the mathematical theory of knots, can characterise complex entangled structures. It will also consider recent approaches in which machine learning methods are used to recognise, classify, and predict knot-theoretic properties.
Minimal surfaces, i.e. surfaces with zero mean curvature, appear in many physical and biological systems, from cellular membranes to butterfly wings. This module introduces the basic theory of minimal surfaces and shows several examples in which such structures arise in nature.
Graphs embedded on surfaces lie at the intersection of combinatorics, topology, and geometry. This module introduces basic concepts such as planar graphs, embeddings on surfaces, and Euler’s formula, and discusses how the topology of the underlying surface influences the combinatorial properties of the graph. We will also consider entanglements and related structures on surfaces.
The series will conclude with an introduction to topological data analysis. Rather than focusing on the theoretical foundations, these sessions will illustrate how topological ideas can be used in practice to explore and visualise complex data.
The seminars are open to bachelor's students, master's students, PhD students, postdoctoral researchers, and faculty members. Talks will be given by speakers from the University of Potsdam and invited guests.
Dates: Tuesdays 12:15-13:45.
Further information is available through the Moodle page. Please contact us if you have any questions andriamana (at) uni-potsdam.de, francesca.bertoglio (at) uni-potsdam.de.
