Michael Wibmer, University of Pennsylvania
“Groups defined by algebraic difference equations”
Difference equations are a discrete analog of differential equations. The algebraic theory of difference equations, also known as difference algebra, enhances our understanding of the solutions of difference equations in much the same way as commutative algebra and algebraic geometry enhances our understanding of the solutions of algebraic equations.
The protagonists in this talk are subgroups of the general linear group defined by a system of algebraic difference equations in the matrix entries. These groups have a rich structure theory, to some extent analogous to the theory of linear algebraic groups.
Groups defined by algebraic difference equations occur naturally as the Galois groups of linear differential equations depending on a parameter. I will explain how structure results for these groups can be applied in the study of the relations among the solutions of a linear differential equation and their transforms under various operations like scaling or shifting.
M3 3103
Refreshments will be served in M3 3103 at 3:30 pm. Everyone is welcome to attend.