Courts have long held that cities can require permits for demonstrations. I'm not sure the permit application can be denied, but the city has to be informed.
Courts do lots of unconstitutional things. They think the Constitution is a list of suggestions to be discarded at the first inconvenience.
I'm not sure the permit application can be denied
That usually depends on how sympathetic the local authorities are to the protesters. Which of course is the complete opposite of the intent of the 1st Amendment. Popular speech requires no protection.
but the city has to be informed
I disagree, but even so a permit is an application to be approved or denied. It is an entire different animal than a notice, which asks no permission.