How to convey your full length paper in conference through slides? I am a PhD student works in computer algebra(Theoretical computer science). I have published one research paper recently, I am currently making slides for the paper. It is my first time and believe me I am struggling a lot. I have spent 4 days but till now not able to convey the idea that I want to deliver to the audience. I have given 30 mins for the presentation. My algorithm is based on 4-5 other algorithm with few lemma and some modification to previous algorithms. I am confused how to make slides such that I can convey my work efficiently.

Should I focus more on modified previous results or on new lemma. Should I first explain them notations and definition or directly go to the results.

Questiom : How to convey your full length paper in conference through slides?

Edit : Audience is Professor and Ph.D students of computer science and mathematics.
In a short face to face presentation, remember that insight is much more important and valuable than detail. People aren't going to remember the detail, and can get it from the paper if they need it, but they will remember if you can show them why your main result is true from a chain of insights.