As noted above, soapstone is pretty inert to heat, although at extreme temperatures it changes to another form useful for electrical insulators. Granite is an aggregate, and can have moisture in its interstices. If a very hot pan is placed on it, the expanding water vapor could cause spalling. Surfaces like Corian are based on aluminum oxide loaded Plexiglass (methyl-methacrylate) and will melt, burn, or otherwise be damaged. I am not sure what resin is used in the so-called quartz counters, but I would follow the advice above and always insulate. Metal counters are pretty insensitive to heat, but if formed over wood, extreme heat could pass through the metal and damage the wood underneath. Tile would seem to be safe, but all hard surfaces are best protected with a hot pad to avoid both scratching and chipping. kas

Heating aluminum foil in an induction field occurs because the foil has electrical conductivity, and the alternating induction field induces a current in it. The more difficult question is why the sensor that is supposed to be present would "detect" that an proper pan was above it when only foil was above it. Aluminum is slightly diamagnetic, but this shouldn't be sensed by a magnet. If the unit detected the foil another way, such as from a reaction field, then it is not designed well, because there are good reasons for not allowing aluminum pans to be heated. However, if a proper pan is present, and someone puts it on aluminum foil, or allows aluminum foil to nestle up next to the pan, then the fault lies with the cook. kas This post was edited by kaseki on Tue, Oct 22, 13 at 11:08

I agree with dan1888 that a slightly warped carbon steel skillet will mostly work in the sense that perfect contact is not required for induction. The distances are not great enough to keep a warped pan from working. But the pan will be sitting on a ceramic smoothtop surface. Depending on how the pan warped, an uneven base might make make the pan prone to spinning, sliding around etc. That difficulty can be fixed with silicon or paper spacers (as described previously by Kaseki and others above) or even with a dish towel under the pan. Of course, those strategies do limit how hot you make the pan. Very high heats (say 500°F) may scorch or ignite or melt a spacer. However, depending on how warped the pan base and how "perfect" you need things to turn out, you might find the warp causes uneven pooling of oil and fats, pancake batters. omelettes. and etc. This will be true on any cooking surface as well as with oven use.

My GE Monogram induction cooktop now has a perfectly circular etched scratch on the front right burner. Until this weekend I had been using an induction compatible stainless $43 Tools of the Trade 10 piece set with clear glass lids and have had no problems. For the first time ever I used an old Le Creuset pot b/c I had guests and needed to cook a lot of pasta. The water boiled over when I lost track of it due to the power and speed of the induction and also b/c without a glass cooktop I had no visual cue to alert me. The bottom of this pot has what looks like a slightly rough cast iron circular bottom before the enamel starts on the curve where the sides of the pot begin. The pot is so heavy that I know I didn't move it around on the burner with all that water in it. All I can imagine that happened is that the water that boiled over caused the pot to hydroplane a bit and that it ground out the circular etch or scratch as it settled down again. I almost cried when I realized that I had done this but the silver lining is that I was the one to damage my beautiful induction baby so I wouldn't have hard feelings toward anyone else---sort of like getting that first scratch on a new car. Also, since it is a mirrored/reflective cooktop and the scratch is within the patterned section of the burner it is not as visible as it could have been. Bottom line for me is that I will be much more careful about water on the cooktop in the future.