Faculty of Science

Login for PhD students/staff at UCPH Login for others

Introduction to Infinity-Categories
Provider: Faculty of Science

Activity no.: 5575-17-07-31
	Enrollment deadline: 28/04/2017

Place	Department of Mathematical Sciences
Date and time	25.04.2017, at: 13:00 - 22.06.2017, at: 15:00
Regular seats	30
ECTS credits	7.50

Contact person	Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser	Rune Gjøringbø Haugseng E-mail address: haugseng@math.ku.dk
Written language	English
Teaching language	English
Semester/Block	Block 4
Block note	Tuesdays and Thursdays from 13:00 to 15:00 - at the 4th floor seminar room (04.4.01).
Exam form	Continuous assessment
Exam form	One internal examiner
Exam details	Participants will each give one 2x45-minute lecture during the course.

Enrolment guidelines After completing the course, the students will have: * Knowledge of the material mentioned in the description of the content. * Skills to read and understand research papers concerning topics discussed in lectures. The following competences: * Have a good overview and understanding of the theory of quasicategories and how they give a useful language for homotopy theory. * Master (at a satisfactory level) the fundamental results covered in the lectures, to the extent of understanding their proofs and being able to interconnect various results. The first part of the course will develop the basics of the theory of quasicategories (equivalences, joins and slices, limits and colimits, the Joyal model structure, fibrations). The second part will cover a selection of more advanced topics in less detail - the exact topics will depend on the interests of the participants, but may include: stable infinity-categories, (co)Cartesian fibrations and straightening, presentable infinity-categories and the adjoint functor theorem, monads and the Barr-Beck-Lurie theorem, symmetric monoidal infinity-categories, infinity-operads, Segal spaces, infinity-topoi. Some familiarity with simplicial sets and model categories is required. Target group After completing the course, the students will have: * Knowledge of the material mentioned in the description of the content. * Skills to read and understand research papers concerning topics discussed in lectures. The following competences: * Have a good overview and understanding of the theory of quasicategories and how they give a useful language for homotopy theory. * Master (at a satisfactory level) the fundamental results covered in the lectures, to the extent of understanding their proofs and being able to interconnect various results. Teaching and learning methods Two 2x45-minute lectures per week. Content The first part of the course will develop the basics of the theory of quasicategories (equivalences, joins and slices, limits and colimits, the Joyal model structure, fibrations). The second part will cover a selection of more advanced topics in less detail - the exact topics will depend on the interests of the participants, but may include: stable infinity-categories, (co)Cartesian fibrations and straightening, presentable infinity-categories and the adjoint functor theorem, monads and the Barr-Beck-Lurie theorem, symmetric monoidal infinity-categories, infinity-operads, Segal spaces, infinity-topoi. Some familiarity with simplicial sets and model categories is required.

Click the search button to search Courses.

See which courses you can attend and when

Jan	Feb	Mar	Apr
May	Jun	Jul	Aug
Sep	Oct	Nov	Dec