Dont know about Bikes, but for cars defintely you run with higher pressures for track use.
Typically you would inflate them by about 10% over standard,
or a little higher than the recommended extended high speed rating.
You would then check your pressures at the end of each session and cap them at some reasonable upper level.
e.g. for my GTA with 225/45/17 I would start at 2.6 bar cold (I normally drive a 2.4 bar cold for the road) and allow to heat to about 2.8 bar.
If they go much over 2.8 bar I would let some out to bring it back down to 2.8 bar.
Generall I only have to adjust after the first session, and normally the pressures are consistant after the other sessions, but some trial and error would be reuqired to find the best pressures to start at - and end up with.
When you start with a higher pressure what actually happens is that your tyres dont get as warm as if you started with a lower pressure - since the firmer tyre side-walls dont scrub as much.
If on the other hand you start with lower pressure than normal, the tyres will heat up very very very quickly due to scrubbing of soft tyrewalls and will achieve very high pressures and then absolutely ruin handling very dramatically.
You also are at risk of pulling the tyre off the rim if your pressures are too low. You might get one or two laps with what appears to be amazing traction with soft tyres, but your tyres will be like jello after it and you will wear them like billy-o.
A correct pressure setting will have the scrubbing of the tyres not going over the tyre wear line marker at the side of the tyre.
i.e. the circle that marks the edge of the sectrion designed to contact the road.
If you pressure is too low then you will scrub right over this line, possibly by an inch or more - you dont want this.
If this happens then increase the pressure to the point where it doesn't happen.
Conversely If no scrub at all is being detected near the line, you could experiment with slightly lower pressure to give more traction.
In a fairly heavily modified GTA on a track that is hard on tyres, I would expect to get 3 to 4 trackdays out of a set of Michelin Pilot Sport 2 road tyres.
Some other reasonable road tyres might wear much much more than that, Good year F1's (GSD3 or asymmetric are good too).
How much you wear tyres at track days when starting out is almost entirely down to how much you are inflicting understeer on your car..
If you ensure that you are making the apex in such a fashion that you can actually release steering lock after making the apex
the strain on the tyres is way less and you will exit the corner way faster - even if you are entering it more slowly initially.
Slow-in fast-out sounds simple, but convincing yourself to do it isn't
Just noticed that a few of you are talking about putting more air in your tyres rather than dropping them by a few PSI. Won't the tyres get much hotter on the track than on the road so if you put more air in you run the risk of them being over inflated once they get hot? All the bike treack days i've been on say to either leave them alone or drop them by 2-3 psi.