I've been doing origami for over a decade now, and have been working on some mathematics behind origami as well. Here are a few talks that I've given on origami:
Origami, Geometry and Galois theory - a Seminar under Mathematics Student Seminar at School of Mathematics, TIFR
The Computational and Algorithmic Aspects of Origami - a Seminar under STCS Student Seminar at School of Technology and Computer Science, TIFR
To Fold or not to fold - Origami Beyond Paper - A TEDxStXaviersMumbai talk in which I decribed my journey as an origamist and mathematician
A heady Addiction of Origami and Mathematics - A Talk in Collaboration with Junoon Theatre at Dr. Bhau Daji Lad Mumbai City Museum
Fold and Behold - A Chai and Why? - Public outreach lecture at Prithvi Theatre, Mumbai