The closest position he's advocating for is to freeze the rent stabilization rate for 5 years while massively ramping up the construction of new apartments to bring rental costs down.
Much of the pushback about Mamdani seems to be a fundamental misunderstanding of the difference betwene "rent control" and "rent stabilization". I think it's extremely rare to see a politician understand the supply/demand aspect of housing costs so well. He really seems to understand these dynamics, certainly better than anyone he's running against.
This is especially relevant in this election, as Cuomo is attacking Mamdani for living in a rent stabilized apartment, suggesting it's hypocritical because he can afford a more expensive apartment. This is deliberately trying to muddy the distinction between "rent stabilized" and "rent controlled" (about half of NY apartments are rent stabilized, and there is absolutely no cultural expectation that people move out when they get a raise, or whatever nonsense Cuomo's suggesting).
Rent stabilization is roughly based on the inflation rate, so, while tenants who've lived in one place for a while might be getting something approximately considered a "sweet deal", it's not the ridiculous scenario rent control can produce. One other relevant distinction, rent controlled units can be passed down to family, keeping the same rent rate. Rent stabilized apartments can also be passed down, but it's the same as if a new tenant was taking over—the price can be reset back to market rate.