Symmetries on symmetric products
Supervisor: Bj酶rn Dundas, email: bjorn.dundas math.uib.no
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Prerequisites: You must have either taken MAT242 or MAT243 or follow MAT243 in parallel with the project.
Description: The starting point for this project will be to study of a specific space: the "nth symmetric product of tori." A torus is what you get by taking the product of a circle S1 with itself a few times.
If, for example, you take the product of the circle with itself, you get the usual torus S1聽脳 S1, which looks like the surface of a doughnut. The symmetric product of a space X is what you get if you consider "the space of all configurations of n identical particles in X." Symmetric products are important in both algebraic geometry and algebraic topology.
The plan is to study group effects and the quotient spaces that arise by identifying "symmetrically equivalent points" on the symmetric products of tori.
What you will learn:
- fibre bundles (topology),
- examples of varieties (algebra),
- symmetries (geometry).
Literature: A literature search will form part of the project.
