#algebraicgeometry — Public Fediverse posts

Tenure-track opening @ U. Colorado Boulder Dept. of Math!

Esp. (but not only) looking for:
algebraic geometry
homotopy theory
foundations
functional analysis
number theory
interdisciplinary collab. b/w math & computer science or the math of quantum physics

https://www.mathjobs.org/jobs/list/27231

Please help spread the word!

#AlgebraicGeometry #HomotopyTheory #AlgebraicTopology #FoundationsOfMath #FunctionalAnalysis #NumberTheory #ComputerScience #Quantum #Math

📚🧮 Oh joy, another thrilling installment of 'Algebraic Geometry Notes' with an awe-inspiring #timeline from 2010 to 2024. 🤓✨ Because who wouldn't want to compare outdated math notes like fine wines in a cellar? Cheers to the riveting world of algebraic updates! 🍷📜
https://math.stanford.edu/~vakil/216blog/ #AlgebraicGeometry #MathNotes #2010to2024 #MathUpdates #GeekCulture #HackerNews #ngated

The Rising Sea: Foundations of Algebraic Geometry Notes

https://math.stanford.edu/~vakil/216blog/

#HackerNews #TheRisingSea #AlgebraicGeometry #MathNotes #Stanford #University #Education

Nine years ago on a defunct platform I wrote this (and I made a big statement, now-deleted, more below)

==== (start quote)
What do you think of this explanation of the Hodge conjecture by Melbourne mathematician Arun Ram?

https://theconversation.com/millennium-prize-the-hodge-conjecture-4243

I think it's great: the right level of metaphor and concrete examples that arise from simple cases of the problem.

[...]

#mathematics #millenniumprize #hodge #algebraicgeometry
==== (end quote)

Last week I was asked to explain off the cuff the Hodge conjecture by a colleague who is an engineer of some kind. I had recalled from a more recent peep into a certain pop-maths book (mentioned in the [...] above) that the author kinda wimped out, leaving the Hodge conjecture for last and then admitting it was rather complicated. I think I was a bit harsh in what I said in the redacted bit. But that may have been because I don't have the expertise in writing for a popular audience, and this certain person very much did, and held themselves to a higher standard of exposition in both detail and clarity than I would have, nine years ago.

I'm also slightly cooler on the metaphor in the linked post — it's still a good metaphor, but it doesn't work so well for me now as when I first wrote the above.

#Macaulay2 is a #ComputerAlgebra System devoted to supporting research in #AlgebraicGeometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992.

Macaulay2 includes core algorithms for computing Gröbner bases and graded or multi-graded free resolutions of modules over quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core algorithms are accessible through a versatile high level interpreted user language with a powerful debugger supporting the creation of new classes of mathematical objects and the installation of methods for computing specifically with them. Macaulay2 can compute Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition of ideals, integral closure of rings, and more.

https://macaulay2.com/