What happens when you mix sulfuric acid with isopropanol?

It depends on the relative concentrations of the acid and the alcohol, and the temperature at which they are reacted.

Typically, the direct reduction of an alcohol by an acid produces an ester. In this specific reaction the expected product would be propyl hydrogen sulfate, aka sulfuric acid propyl ester. Esters and their "mother alcohol", in turn, react to form ethers, in this case dipropyl ether, with the acid and water as a byproduct.

This esterification reaction is readily reversible; the ether will crack water to reform the alcohol, and the ester will hydrolyze in the water to reform the acid and alcohol. By Le Chatelier's principle, these reactions will form an equilibrium between the acid, alcohol, ester and ether. The ether can be recovered by gentle heating to distill it, which shifts the equilibrium leading to sustainable production of the ether. The reaction can be quenched with water, which will hydrolize the ester back into the alcohol and acid, or by adding a strong base to neutralize the acid (in either case the ester is consumed by this process).

At very high concentrations of sulfuric acid (that would be called "fuming sulfuric acid" or oleum), the acid will dehydrate the alcohol (removing its hydroxyl and an additional hydrogen, forming a water molecule to balance the water and sulfate ions) to form an alkene, in this case propylene. This is again a reversible reaction; adding water to the mixture will lower the concentration of sulfuric acid and cause acid-catalyzed hydration of the propylene to reform propanol.