Title: Equivariant Borel liftings in complex analysis 
Abstract:
Some time ago, Benjy Weiss proved existence and abundance of non-trivial translation-invariant
probability measures on the space of entire functions. Another suggestion of Weiss was to try
to get rid of the notion of measure in ergodic theory, and to see what remains. This idea
was at the origin of Borel dynamics.
My talk will be based on joint work with Slutsky and Wennman (arXiv:2507.12058), in which we
combined both ideas. Our main result states that there exists a Borel map assigning to each
non-periodic positive divisor D an entire function F_D such that the divisor of zeroes of F_D
is D and  F_{D-w}(z) = F_D (z+w), for any complex w. Here, Borel measurability cannot be strengthened
to continuity. The two key ingredients are the Runge approximation theorem and the existence of
``Borel toasts'', which are Borel counterparts of Rokhlin towers from ergodic theory.
Curiously, in other instances, equivariant Borel liftings may not exist. For instance, in the above result,
non-periodicity cannot be omitted. Another example is the non-existence of an equivariant Borel
primitive, i.e., a solution to f'= g in entire functions. 
If time permits, I will also discuss equivariant Borel liftings in PDEs.