Short answers, pulled from the story.
Amir Tamerlane founded the Timurid Empire in 1370 after conquering several Ilkhanate successor states. His strategy involved sparing local artisans when capturing a city and then deporting them to his capital of Samarkand.
Turquoise and blue tiles formed intricate linear patterns on the facades of major buildings like the Gur-e Amir mausoleum in Samarkand. These structures featured double domes perfused with brilliant colors and axial symmetry characteristic of all major Timurid edifices.
Ali Qushji developed astronomical physics independent from natural philosophy and provided empirical evidence for Earth's rotation in his treatise Concerning the Supposed Dependence of Astronomy upon Philosophy. The Plate of Conjunctions was invented as an analog computing instrument used to determine planetary conjunction times.
Timurid silver-inlaid steel is often cited as being of particularly high quality among metal artifacts produced during this period. Steel iron brass and bronze were commonly used as mediums for creating these durable objects.
Following the decline of the Timurid Empire in the late 15th century the Ottomans Safavid dynasty and Mughal India co-opted Timurid artistic traditions. These Gunpowder empires adopted the architectural styles scientific methods and artistic techniques developed under Tamerlane and his successors.