Title of the course: Expected topology of random simplicial subcomplexes
Instructor: Assoc. Prof. Nermin Salepci
Institution: Université Claude Bernard Lyon 1, Institut Camille Jordan
Dates: 12-18 August 2024
Prerequisites: Topology and algebraic topology. Basic (discrete) probability.
Level: Graduate
Abstract: We will describe a method to construct subcomplexes of the first barycentric subdivision of a finite simplicial complex. We then calculate the expected topology (e.g. expected Euler characteristic and expected Betti numbers) of these subcomplexes. By iterating the procedure we will look at the asymptotic behavior. The course will start with quick recall of the basics: simplicial complexes, barycentric subdivisions, simplicial homology, Euler characteristics and Betti numbers.
Language: TR, EN
Textbook: For related algebraic topology topics : J.R. Munkres “Elements of Algebraic Topology”. For random topology article by me with J.-Y. Welschinger titled “Asymptotic topology of random subcomplexes in a finite simplicial complex”.