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Applied Algebraic Topology SemesterWiSe 2022 / 23 Lecturer Clara Löh Type of course (Veranstaltungsart) Vorlesung German title Angewandte Algebraische Topologie Contents The tools and methods from algebraic topology have a wide range of applications to other fields and to real-world problems. Graphs are combinatorial structures that can be used to model connectivity of various kinds, e.g., connections between people in social networks, genetic proximity in biology, or dependencies between software components. Simplicial complexes are a higher-dimensional generalisation of graphs and thus allow for more fine-grained models, e.g., for discrete approximations of geometric shapes, connectivity of high-dimensional data, decentralised computations in sensor networks, configuration spaces for robots, or dependencies between agents in distributed systems. Algebraic topology is mainly concerned with geometric features that are invariant under a special type of deformations: homotopies and homotopy equivalences. A classical (and computable) example of a homotopy invariant of simplicial complexes is simplicial homology. Moreover, the language of homotopy theory also found a completely different type of applications in the foundations of mathematics and computer science. In this course, we will learn the basics of simplicial complexes, simplicial homology, and homotopy invariance. We will explore modelling and real-world applications of these notions and invariants. Whenever feasible, we will also look at implementation matters. Literature Literature will be announced at the beginning of the course and lecture notes will be provided. Recommended previous knowledge All participants should have a firm background in Analysis I/II (in particular, basic point set topology, e.g., as in Analysis II in WS 2011/12), in Linear Algebra I/II, and basic knowledge in group theory (as covered in the lectures on Algebra). Experience in Geometry/Topology or Algebraic Topology is helpful, but not really necessary. Programming experience is helpful, but not necessary. Time/Date Tue/Fr 8:30-10 Location M 104 Course homepage https://loeh.app.ur.de/teaching/aat_ws2223 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MGAGeo ECTS 9 ECTS |