The short answers:
Will global warming cause more hurricanes? No.
The number of hurricanes seems to be pretty constant -- 2005 was an unusualy active year, but there isn't a trend that correlates with sea surface temperature (SST).
Will global warming cause stronger hurricanes? Yes.
A global study of all the differnt ocean basis shows a statistically significant trend of increasing SST that correlates with an increase in hurricane intensity.
Aside: here we get into the disagreements. There are some prominent people who say that it's just due to natural variability in atmospheric or thermohaline circulation, but the speaker showed results from a couple papers (which are currently in press) that show (1) math (some crazy Bayesian multi-entropy thingy) says SST is the best explanation for most of the variation in hurricane intensity; and (2) the variations in thermohaline circulation actually have the wrong sign to account for it. On top of that, there are good theoretical reasons to expect SST to increase hurricane intensity, and numerical models also show it.
There are some NOAA climate variability patterns that appear to explain the hurricane variability patterns, but it turns out that those are coming from EOFs that were generated from data that wasn't detrended, which creates a spurious long-term oscillation mode. So, as they say, "the proponderance of the evidence" supports the idea that global warming increases hurricane intensity.
So what causes hurricanes to form? A "negative stretching deformation".
That's only part of it; we don't really know why they form because, well, it's a hard problem, but this is an important new piece of the whole hurricane genesis puzzle.
The traditional conditions for hurricane formation seem to be wrong, because the conditions occur far more frequently than hurricanes actually do, plus there's no physics behind several of them. The new criteria he theorizes:
A negative stretching deformation of the zonal flow (dU/dx negative) causes energy from Rossby waves to concentrate as the wave group velocity (which transports energy) drops to zero due to doppler shifting. In other words, you get these easterly waves coming off a continent, and when they hit a region where the winds are reversing, their wavelengths get shorter and the energy they're carrying gets all piled up in that spot. And having a whole bunch of energy in one spot in the atmosphere is what leads to hurricanes. So a "negative stretching deformation" is the atmospheric condition necessary for a hurricane to form, and in a way, that's "what causes it".
And I won't claim to totally understand it -- but I mostly followed, and it was a neat thing to be able to write about!