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Continuous K-theory, Dualizable and Rigid Categories
Provider: Faculty of Science

Activity no.: 5566-24-07-31
Enrollment deadline: 15/05/2024
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time10.06.2024, at: 09:00 - 14.06.2024, at: 16:00
Regular seats100
ECTS credits2.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJesper Grodal    E-mail address: jg@math.ku.dk
Teaching languageEnglish partially in English
Block noteDuration: 5 days
Course workload
Course workload categoryHours
Preparation34.00
Lectures15.00
Practical exercises10.00
Theoretical exercises10.00
Sum69.00
Content
The course aims to introduce the participants to new methods in, and applications of algebraic K-theory, based on Efimov's recent breakthroughs about dualizable categories and localizing motives.

Learning outcome
Knowledge:
• The students will acquire an understanding of the fundamental results surrounding continuous K-theory and dualizable categories;
• The students will acquire a vision for the potential applications of continuous K-theory to neighbouring fields.

Skills:
• To be able to use the acquired knowledge to perform computations with continuous K-theory.
• To be able to use the acquired knowledge to perform computations with dualizable categories.

Competences:
• To be able to produce independent proofs of results involving continuous K-theory.
• To be able to produce independent proofs of results involving dualizable categories.

Target group
The course is designed for PhD students and early career researchers who want to learn about the latest developments in the theory of localizing motives and neighbouring fields. Participants should have some basic knowledge of K-theory.

Teaching and learning methods
The masterclass will consist of three lecture series, shedding light on the three different aspects of Continuous K-theory, dualizable and rigid categories.

This will be accompanied by exercise sessions and informal discussion sessions in which the participants can practice the computational methods which are discussed theoretically in the lectures.

Lecturers
Alexander Efimov, Steklov Institute for Mathematics
Thomas Nikolaus, Münster University
Dustin Clausen, IHES Paris

The guest lecturers are experts and will each describe the main current research themes in this area:

Efimov is at the origin of these breakthroughs and he will give a course on his fundamental definitions and results (continuous K-theory, the rigidity of the category of localizing motives, and his results on categorifications of algebraic KK-spectra);
Thomas Nikolaus is exploring applications of these new techniques to geometric topology and sheaves and will give a course on these ideas (the categorification of the assembly map for A-theory);
Dustin Clausen is exploring the interaction between Efimov's new theories and condensed mathematics and will give a course on this (K-theory of categories of nuclear modules, K-theory of liquid C-modules).

Each will give a lecture series of 5 lectures.

Remarks
For registration and more information, please visis the course page: www.math.ku.dk/english/calendar/events/masterclass-continuous-k-theory

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