TSVP Talk: "Numerically Verified Proofs in Geometry and Beyond" by Daniel Platt

Title: Numerically Verified Proofs in Geometry and Beyond

Speaker: Daniel Platt, Imperial College London

Abstract: When solving an equation like x^2-2=0, a computer will readily produce an approximate solution x=±1.4142. The idea of numerically verified proofs is to use a fixed point theorem to prove that a genuine solution exists near this approximate solution. For polynomials, there are other tricks that one could use. But in recent years, computers have become powerful enough to use this approach for solving PDEs where it can crack problems no other approach can. In the talk I will explain how this technique works abstractly, and then apply it to a PDE on the 2-sphere called the "Nirenberg problem" in some detail (see arXiv:2603.29544). Numerically verified proofs are a very general technique that can be applied to many different problems, and in the last five minutes I will mention suitable problems in geometry. I will also mention suitable problems in other areas about which I know little.

Profile: Daniel is a research fellow at Imperial College London working on numerical methods applied to differential geometry. He obtained his PhD in differential geometry from Imperial College in 2022 and since then worked as postdoc at King's College London and Imperial College London.

Language: English

Target audience: General audience/everyone at OIST and beyond.
Freely accessible to all OIST members and guests without registration.

This talk will also be broadcast online via Zoom:
Meeting ID: 993 1216 5065
Passcode: 603487

※ Please note that this event may be recorded and the videos uploaded. In addition, photos may be taken during the event. These are intended for publication online (the OIST website, social media, etc.)※