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Regular version of the site
2020/2021

Research Seminar "An introduction to Factorisation Homology"

Type: Optional course (faculty)
When: 3, 4 module
Open to: students of one campus
Language: English
ECTS credits: 6

Course Syllabus

Abstract

Factorisation homology is a homology theory for manifolds, defined for non-linear coefficients. Among its various applications are those to the topology of configuration spaces, to Hochschild theory, and to topological field theory.
Learning Objectives

Learning Objectives

  • Students will take turns lecturing on the basic theory of factorisation homology, as well as its applications.
Expected Learning Outcomes

Expected Learning Outcomes

  • Students will learn the basics of factorisation homology, while improving their presentation and writing skills.
Course Contents

Course Contents

  • Review of homotopical category theory (`infinity categories')
  • Definition of little disks operads and its generalisations
  • Topology of configuration spaces
  • Factorisation algebras for stratified spaces
  • Definition of factorisation homology and basic examples
Assessment Elements

Assessment Elements

  • non-blocking Students notes of presentation in TeX
  • non-blocking Student presentation
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.5 * Student presentation + 0.5 * Students notes of presentation in TeX
Bibliography

Bibliography

Recommended Core Bibliography

  • Наглядная топология, Прасолов, В. В., 2006

Recommended Additional Bibliography

  • Lurie, J. (2009). Derived Algebraic Geometry VI: E_k Algebras.