The Future Circular Collider with electron positron beams
colliding with the CMS energy being 80-450GeV
(FCCee, one of several projects considered for construction in CERN)
thanks to very high luminosity would provide true "Giga Z " operation mode,
in which LEP statistics of several years would be reproduced within minutes!
The experimental precision of the standard observables,
like cross sections, asymmetries etc. would be improved
by factor up 200. This would open enormous opportunities
for searching indirect signs of New Physics.
I shall comment on the biggest challenges in calculating
various Standard Model predictions (electroweak and QED)
with the precision factor 5-100 better than
in the present state of art inherited from the LEP era.