# ANAGRAMS

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.