In Peninei Halacha, Rav Melamed permits koshering and using induction cooktops under certain conditions (here):
Induction cooktops: The surface on which the pots are placed is like smooth, impervious glass. However, unlike ceramic burners, in which the heat source is within the ceramic surface, in induction cooktops the heat source is in the pot, which heats up by means of a magnetic field. From the pot, the heat spreads to the food cooking within it and to the surface on which it is standing. Ḥametz is liable to be absorbed into the cooktop via food that overflowed from the pot, some of which can get stuck to the base of the pot and continue to heat up along with it. Such cooktops are therefore kashered by cleaning them and pouring boiling water over them. Kashering them from the food that overflowed and got stuck to the bottom of the pot is based on the principle of ke-bole’o kakh polto: wet the bottom of the pot when they are empty, and heat them up on the cooktop for about 15 minutes. (Below, in section 12, the obligation to kasher glassware is discussed.)
In section 12 (here) Rav Melamed makes a distinction between Ashkenazim and Sephardim vis a vis glass and concludes that:
Many Sephardim follow the lenient opinion and kasher glassware by rinsing it only, and many Ashkenazim have the custom not to kasher glassware. In practice, however, it seems that the middle position, according to which glassware has the same status as metal kelim and can be kashered by means of hagala, is primary. Those whose family custom is to be lenient may maintain their custom, and those whose family custom is to be stringent should maintain their custom.
i.e., Rav Melamed brings a distinction between Sephardim and Ashkenazim. It is acceptable for Sephardim to kosher and use like regular glass, and that ("primarily") Ashkenazi psak would allow it as well.
To counter this, the OU does not allow kashering of glass stovetops, but provides a solution to using one in any case (here):
Glass Stovetop: A glass stovetop cannot be kashered, and therefore must be dealt with as follows:
- Clean the stovetop surface well and do not use for 24 hours.
- During Pesach, pots should not be placed directly on the stove surface, but
rather an aluminum (or other metal) disk should be placed directly
under the pots.
One should not cover the entire glass top surface, as this might cause it to overheat and crack.