Elliptic PDE (Connor Mooney) | Ep. 7

Connor Mooney is an Assistant Professor of mathematics at UC Irvine and an expert in partial differential equations. We talk about his work and what it means to study PDE in the 21st century.

0:00 Connor's academic background
7:06 What is a PDE? (Heat equation, Einstein equation)
17:30 What is an ELLIPTIC PDE? (Minimal surface equation)
31:25 What sort of question in PDE does Connor try to answer?
41:40 The different views towards PDE of mathematicians and physicists; the Navier-Stokes equations
55:30 What techniques does Connor use in his work? Building sample solutions, using these to control unknown solutions through the maximum principle. "Double zipper" approach to testing hypotheses and proving theorems. Linearization.
1:05:45 What does it mean for solutions to be "close"? The right way to measure; role of dimension
1:13:03 Some different approaches to PDE
1:24:40 How undergraduates can get into PDE
1:37:23 PDE for applications. Influential mathematicians in history.
1:46:17 What's next? Problems on the horizon.
1:54:25 Does career pressure lead to more incorrect papers? Choosing good problems.

[lowerbound]

Packed with great stuff. Appreciate both questions and answers, thanks✌✌