apr14_23

Zeta functions in asymptotic algebra I: subobject growth

Tobias Rossmann

University of Galway, Ireland

Over the past decades, the study of zeta functions arising from algebraic
counting problems has evolved into a distinct branch of asymptotic algebra.
An appealing feature of this area is that it constitutes a meeting ground
for several different mathematical subjects such as algebra, combinatorics,
geometry, and logic. My first talk will be a biased introduction to this
area, in particular to the study of zeta functions enumerating subobjects
(e.g. subgroups or submodules).

Zeta functions in asymptotic algebra II: orbits and conjugacy classes

Tobias Rossmann

University of Galway, Ireland

My second talk will be motivated by but logically independent of the first.
I will focus on recent developments surrounding zeta functions enumerating
(mostly linear) orbits of unipotent groups. A key theme will be the
development of tools for proving the (somewhat surprising) absence of
geometric features (“uniformity”) in certain situations.