Atiyah comes through with another solution to a long unsolved problem, proving the non-existence of a complex structure on [math] S^6 [/math]:
arxiv.org
What is Veeky Forums reading? What problems are you working/stuck on? Progress on research/theses?
why is grothedieck bald
To keep the government out
do we have confirmation that Atiyahs proof is accepted or not?
The dude is getting old and his abstract seems to suggest he didn't need any new ideas to solve it. Seems strange that the proof would of been missed for this long.
Holy shit, he proved it in one page. I hope this is legit, but there are very few premises in his argument. It's really straightforward. Goddamn!
Atiyah's a cool guy. He solves problems and doesn't afraid of anything!
>What is Veeky Forums reading?
Cohomology of Sheaves by Birger Iversen
>What problems are you working/stuck on?
I'm trying to construct a way to classify abelian categories using categories of modules as my tool. How to generalize this from small subcategories to cover general abelian categories is still a mystery.
>Progress on research/theses?
I have yet to recheck my arguments for the classification of small abelian categories, but it seems to be done.
Thank you OP.
This is inspiring.
how do you classify abelian categories use cats of modules?
Is this some sort of coherent sheaves type business?
>What is Veeky Forums reading?
Introduction to Representation Theory by Etingof
Complex Analysis by Dolbeault
Begriffsschrift by Frege
>What problems are you working/stuck on?
Finding good problems to work on... I'm pretty bored
>Progress on research/theses?
Not working on anything specific atm
The small ones I managed to classify using the Mitchell embedding. As I mentioned, I need to recheck that everything is correct up to this point, but I do believe I have been able to use equivalences of module categories between their subcategories, and, later, between the embedded abelian categories. The problem is that it is still very restrictive, as there is the limiting assumption of the categories being small.