Thanks to Indu Nagarajan for organizing the program and getting the poster made!
The Ragam Thanam Pallavi (RTP for short) is the pinnacle of a Carnatic concert, testing the limits of the creativity of the main artist(s), and the anticipatory and accompanying skills of the accompanists. It resembles the format of a Hindustani piece, beginning with slow alaap and gradually getting faster. RTPs in carnatic concerts can be done extremely quickly (I’ve heard Shashank and Ravikiran do 10-15 min RTPs at the Music Academy before!) or slowly and elaborately. Mudhra once held a concert series of “RTP concerts” where the only item in a 3-hour concert was one RTP!
Pallavis can also be very simple in structure, being in one ragam and a simple thalam (rhythmic cycle), or they can be complicated, featuring several ragams and a complex thalam. Pallavis not set to the usual chatusra nadai (4 counts per beat) are called nadai pallavis. These are obviously much more complex. As is the norm with any Carnatic concert, the violin and mrudangam artists generally do not have any idea beforehand what the vocalist (or veena) will do!
EDIT: Found these on Youtube: