# Algebra and geometry research

We research equations and shapes, and their associated properties, structures and symmetries.

Algebra and geometry are interlinked in multiple ways: roughly speaking, algebra provides the language and geometry the intuition.

Our research strongly reflects these interconnections, relying upon advanced algebraic methods in geometry as much as geometrical ideas in algebra. Our research in algebraic geometry meets with quiver representation theory and homological algebra, while work in smooth and discrete differential geometry ties in with algebraic and Lie groups, discrete groups, and combinatorics.

There are also interactions with number theory in algebraic geometry, with geometric analysis and ergodic theory in differential geometry, and with integrable systems and mathematical physics.

We have a regular and lively Geometry seminar with a strong outward-looking flavour and, from time to time, Bath plays host to the famous wandering COW algebraic geometry seminar. We also host the Group Pub Forum community pages.

Our research in algebra and geometry can be arranged under four broad headings:

- algebraic geometry
- differential geometry and Lie theory
- group theory
- representation theory and homological algebra