Topology Seminar: Yuri Burda
Topic
Topology meets essential dimension
Speakers
Details
The talk will be an extended advertisement of a program to apply topological ideas to computation of essential dimension of groups.
The essential dimension of a group G measures to what extent every generically free action of G on an algebraic variety can be "compressed". For the symmetric group S_n, the essential dimension is directly related to the classical question how much an algebraic equation of degree n can be simplified by a rational change of variables.
I will introduce a topological approach to obtaining lower bounds on essential dimension. I will then survey some (non-topological) advances in theory of essential dimension and discuss some parallels in topology. Finally I will speculate on the possibility to relate results in the theory of topological group actions and results on essential dimension in a way that might benefit both fields.
The essential dimension of a group G measures to what extent every generically free action of G on an algebraic variety can be "compressed". For the symmetric group S_n, the essential dimension is directly related to the classical question how much an algebraic equation of degree n can be simplified by a rational change of variables.
I will introduce a topological approach to obtaining lower bounds on essential dimension. I will then survey some (non-topological) advances in theory of essential dimension and discuss some parallels in topology. Finally I will speculate on the possibility to relate results in the theory of topological group actions and results on essential dimension in a way that might benefit both fields.
Additional Information
Location: ESB 4127
Yuri Burda, UBC
Yuri Burda, UBC