Student seminar

## Goal

There is a myriad of dimension functions in (homological) algebra, geometry and the theory of quadratic forms. There is no well-defined notion of dimension function, but let's say it is a numerical invariant of a ring, module or field. The goal would be to discuss some of these, and wherever applicable show how they are related.

The format of this seminar is different from the others:

- talks are somewhere between 15 minutes and 1 hour
- people can give several talks (or discuss several related dimensions at once)
- mostly definitions and facts, no difficult proofs
- provide pointers to the literature

## Schedule

- February 7
- Algebraic dimensions
- in G.017, at 10h00
- lectures by:
- Hoang Van Dinh: Krull dimension and transcendence degree (notes)
- Dennis Presotto: Gel'fand–Kirillov dimension (notes)
- Nikolaas Verhulst: Goldie (or uniform) dimension
- Julia Ramos González: Dimension of triangulated categories (notes)

- February 14
- Geometric dimensions and dimensions for quadratic forms
- in G.017, at 10h00
- lectures by:
- Erik Rijcken: Homological dimensions (notes)
- Pieter Belmans: Depth, and measuring singularities (notes)
- Andrew Dolphin: $u$-invariant, level, Pythagoras number

## References

In due time I might add these.

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