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Algebraic Topology and Homotopy Theory Lab
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The lab studies algebraic K-theory, which assigns a topological space to each ring.
AboutAbout the lab
Linear algebra over rings that are not fields
Prof. Hesselholt studies algebraic K-theory and algebraic topology.
In algebraic K-theory, a topological space is assigned to a ring, and its homotopy groups are called the algebraic K-groups.
Understanding the structure of these groups is a deep problem, and in some cases it is equivalent to a conjecture in number theory.
Topics listed for the small-group classes in the master's program include de Rham cohomology, characteristic classes, and algebraic K-theory.
Key terms
- Ring
- A generalization of a number system in which addition, subtraction, and multiplication are possible. A ring in which division is also possible is called a field.
- Homotopy group
- A group obtained by classifying loops or spheres in a space, treating those that can be continuously deformed into one another as the same.
- Topological cyclic homology
- A theory used in the study of algebraic K-theory. It can be thought of as a generalization of the characteristic polynomial in linear algebra.
ResearchResearch themes
The professor specializes in algebraic K-theory (in particular topological cyclic homology) and algebraic topology (in particular equivariant stable homotopy theory and high-dimensional manifolds). Generalizing linear algebra to rings that are not necessarily fields requires new mathematics, and algebraic K-theory is a theory that arose from this need.
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MembersFaculty
- ProfessorLars Hesselholt
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Topology joke” Keenan Crane and Henry Segerman / CC BY-SA 3.0 (cropped)
- Algebraic K-theory: “Torus vectors radial” RokerHRO / CC BY-SA 3.0 (cropped)
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