Short answers, pulled from the story.
Sir Thomas Young coined the term Indo-European in 1813 to describe a family of languages spanning from the Indian subcontinent to Europe. Before this moment, scholars proposed various alternative names without reaching consensus.
Early alternative names included Scythian proposed by Marcus Zuerius van Boxhorn in 1647 and Japhetic introduced by Rasmus Christian Rask in 1815. Other terms such as Indo-Germanique established by A. Pictet in 1836 and Germanisch introduced by Julius von Klapproth in 1823 also appeared in historical scholarship.
Sir William Jones delivered a lecture in India in 1786 which was published in 1788. He postulated that Sanskrit bore a stronger affinity to Greek and Latin than could have been produced by accident and identified six branches including Persian, Germanic and Celtic.
The Kurgan hypothesis links language history to archaeology through work by J. P. Mallory who published In Search of the Indo-Europeans in 1989. Marija Gimbutas contributed archaeological work while Colin Renfrew also studied the field alongside genetic evidence from Luigi Luca Cavalli-Sforza.
Major research centers exist across Europe and North America with Innsbruck hosting Hannes A. Fellner and Ivo Hajnal and Vienna including Melanie Malzahn and Laura Grestenberger. Institutions such as Oxford and Cambridge host James Clackson and Andreas Willi while Cornell Harvard UCLA and Texas feature scholars like Benjamin W. Fortson IV and Hans Heinrich Hock.