As Konya was the site of many of his most important teachings, it's also the city that he was ultimately buried in. He died here in 1273, though his teachings would suggest that rather than use the word "death," perhaps the word "rebirth" would be more appropriate. He referred to the day of his death as "Şeb-i Arûs," or wedding day, ie the day he would be wed to God.
To this day, every December the day of his death is marked as Şeb-i Arûs and a week-long celebration takes place in the city of Konya, with travelers coming from all over the world to partake in and watch the sema ceremonies, whirling dervishes, and prayer hymns.
Those who adopt Rumi's doctrine of sufism are called Mevlevi or dervishes, and they whirl around in a beautiful ceremony referred to as a Sema ceremony in which they whirl and turn in a dance making themselves one with the Earth. This is the ritual that Rumi himself performed in the streets of Konya before his death.