## Algebraic Geometry Seminar: Yuri Burda, University of Toronto

- Date: 11/21/2011

University of British Columbia

**Abstract: **

Topological essential dimension of a covering is the

minimal dimension of a base-space such that the original covering can be

induced from some covering over this base-space.

We will see how to compute the topological essential dimension for coverings over tori.

Surprisingly this question turns out to be useful in obtaining

estimates in Klein's resolvent problem: what is the minimal number k

such that the equation z^n+a_1z^n+...+a_n=0 with complex coefficients

a_1,...,a_n can be reduced by means of a rational substitution

y=R(z,a_1,...,a_n) to an equation on y depending on k algebraically

independent parameters.

We will also obtain some bounds in the analogue of this question

for other algebraic functions and get a sharp result for functions on

C^n unramified outside of coordinate hyperplanes.

3:10pm - 4:10pm in WMAX 110.