Intrinsic definition of the symbol of a differential operator
Discover the elegant, coordinate-free definition of differential operator symbols through a homological perspective, revealing deep connections in mathematical analysis.
The main result
Dear Reader, recently, I learnt that the symbol of a differential operator has a coordinate-free definition with a slight homological flavour. I will leave it below for a curious reader:
Please enjoy it without moderation!
Dr. Denys Dutykh
Associate Professor of Mathematics
Khalifa University of Science and Technology, Abu Dhabi, UAE
Related Posts
Interim Guidance on the Use of AI Tools in Postgraduate Studies and Research
Interim guidance sent to the postgraduate students of our College on using AI tools in coursework, research and the thesis, written in the week of the Navier–Stokes announcement.
The Cayley–Dickson Staircase: What Each Doubling Costs
The Cayley–Dickson staircase is usually presented as far as the octonions. One step further, at the sedenions of real dimension 16, alternativity, division and the multiplicative norm all fall at once.
From Gauss–Lucas to de Bruijn–Springer
Gauss–Lucas puts the roots of the derivative inside the convex hull of the roots. De Bruijn and Springer conjectured in 1948 that they are pulled inward on average — it took 55 years and two proofs.