Final answer:
The mother church designed by Giacomo da Vignola and Giacomo Della Porta in 1575 is known as Il Gesù, featuring The Triumph of the Name of Jesus ceiling fresco by Giovanni Battista Gaulli (Il Baciccio).
Step-by-step explanation:
The mother church designed by Giacomo da Vignola and Giacomo Della Porta in 1575 is known as Il Gesù. This iconic church is located in Rome and was consecrated in 1584. Inside this magnificent church, there is a ceiling fresco titled The Triumph of the Name of Jesus, which was created by Giovanni Battista Gaulli, also known as Il Baciccio, between 1672 and 1685. The church of Il Gesù is a prime example of early Baroque architecture and played a significant role in influencing the style of churches in the period that followed. Its design and construction showcase the innovative approaches to space, volume, and perspective that characterized the Baroque movement in the arts.