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Combinatorial Hodge Theory
Provider: Faculty of Science

Activity no.: 5546-20-07-31 
Enrollment deadline: 15/04/2020
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time20.04.2020, at: 09:00 - 19.06.2020, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserKarim Alexander Adiprasito    E-mail address: ka@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupC
Exam formOral examination
Exam formCourse participation
Exam detailsI will occasionally give exercises in class, recitation/exercise session will focus on the basic background.
Course workload
Course workload categoryHours
Lectures36.00
Preparation143.00
Exam27.00

Sum206.00


Content
Modern algebraic geometry mostly developed based on the questions arising in arithmetic. Around this context, conjectures and theorems were developed rather successfully. Recent years have seen the same happen in a combinatorial context, that is, the study of discrete objects without an underlying arithmetic structure.

I will review some of these developments, focusing on

- McMullens combinatorial model for Chow rings

- the solution of the Kazhdan-Lusztig positivity conjecture and the work of Elias-Williamson

- the solution to the g-conjecture

If time permits, we shall also discuss relations to Sela's algebraic geometry on the free group.

Learning outcome
Knowledge:
To display knowledge of the course topics and content, at the level of a beginning researcher.

Skills:
To be able to use the acquired knowledge to perform computations.

Competencies:
To be able to produce independent proofs in extension of the acquired knowledge.

Literature
No textbook, a selection of articles will be provided at a later point. Generally, most of the course follows arxiv:1812.10454

Teaching and learning methods
4 hours lectures and 3 hours exercises/recitation for 3 weeks

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