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location Adelaide, Australia
age 30
visits member for 5 years
seen 5 hours ago

Pure mathematician interested in category theory and foundations.


2d
comment Relation between $BG$ in topology and in algebraic geometry
@AntonFetisov ...and there's probably also a clever way to see it via Kan extension along the functor Sch^op --> Top^op.
2d
comment Relation between $BG$ in topology and in algebraic geometry
@Qfwfq - BG gives a topological stack by Yoneda, via sheaves on Top. *//G is a topological stack of groupoids. They have the same homotopy type (in the sense that the homotopy colimit of the nerve of *//G is a BG), but *//G lifts to, for instance, a differentiable and even a holomorphic stack. They are definitely not equivalent in the 2-category of topological stacks.
2d
comment Relation between $BG$ in topology and in algebraic geometry
@AntonFetisov you can take the analytic topology on the $\mathbb{C}$-valued points of the groupoid in schemes, and get a topological groupoid: this presents a topological stack. One can take any reductive algebraic group and consider the same comparison.
Nov
17
comment Calculation of Shannon and Simpson Index as a function of time
All I can suggest is ask a question in meta, or post an answer on the thread I liked asking for reopen votes.
Nov
17
comment Calculation of Shannon and Simpson Index as a function of time
I'm not familiar with this area of mathematics to make a judgement. You can raise a reopen request at meta.mathoverflow.net/questions/223/requests-for-reopen-votes, but please explain clearly why this should be reopened. Ideally there should be enough information in the question above as to your background, what you've tried, why this question is being asked, anyway.
Nov
14
comment Grothendieck -sad news
Meta: meta.mathoverflow.net/questions/1978/grothendiecks-passing
Nov
14
comment Grothendieck -sad news
The amount of mathematics just alluded to is the same order of magnitude as the classification of finite simple groups. This doesn't count thousands of pages written in the 1980s as I allude above.
Nov
14
comment Grothendieck -sad news
"...The project’s final page count, including the twelve volumes known as SGA (Seminaire de Geometrie Algebrique) and the eight known as EGA (Elements de Geometrie Algebrique) approached 10,000 pages. The force and clarity of Grothendieck’s unique vision scream forth from nearly every one of those pages, demanding that the reader see the mathematical world in a new and completely original way — a perspective that has proved not just compelling, but unspeakably powerful."
Nov
14
comment Grothendieck -sad news
@JosephO'Rourke And some good comments here: thebigquestions.com/2014/11/13/the-rising-sea by Steve Landsburg "He dominated pure mathematics not just through the force of his ideas — ideas that seemed eons ahead of everyone else’s — but through the force of his personality. When, around 1960, he announced his audacious plan to solve the notoriously difficult Weil conjectures by first rewriting the foundations of geometry, dozens of superb mathematicians put the rest of their careers on hold to do their parts. ... "(cont)
Nov
14
comment Grothendieck -sad news
@JosephO'Rourke solving a lot of problems in functional analysis, then once moved over to algebraic geometry, completely revolutionising the field (no pun intended) so that the Weil conjectures could be proved. Invented a lot of category theory just on the side. Then rethinking, after he left his job at the IHES, the foundations of homotopy theory and higher category theory. For this, see: Pursuing Stacks, Les Derivateurs, still unpublished, but containing ideas that lead to e.g. Voevodsky's proof of the Milnor and Bloch-Kato conjectures using motivic homotopy theory.
Nov
14
comment Grothendieck -sad news
"What was Grothendieck's greatest contribution to mathematics overall?" Bit subjective, perhaps.
Nov
13
awarded  Yearling
Nov
12
comment Calculation of Shannon and Simpson Index as a function of time
Though it may not be what you are looking for, you may be interested in Tom Leinster's work on diversity: maths.ed.ac.uk/~tl
Nov
12
comment Synthetic vs. classical differential geometry
@user59001 it's not anything to do with model theory (see plato.stanford.edu/entries/model-theory)
Nov
11
comment When does a leaf space admit a (non-Hausdorff) manifold structure?
A manifold has a foliation when it has a collection of foliation charts see e.g. en.wikipedia.org/wiki/Foliation#Definition.
Nov
11
comment When does a leaf space admit a (non-Hausdorff) manifold structure?
Well, one can remove the connectedness condition, and have a theorem that says foliations with connected leaves are the same as those defined by subbundles. As for "remembering" which components belong to which leaves, you just have disconnected manifolds L_i with inclusions L_i -> M, indexed by some set I. There's no magic in trying to figure out all the pieces :-) In the groupoid case it's obvious: in the same orbit=in the same leaf.
Nov
11
comment When does a leaf space admit a (non-Hausdorff) manifold structure?
But why is the definition like that? What theorem fails? If every foliation that arises from a subbundle has connected leaves, that's no reason to demand foliations always have connected leaves, since there are natural foliations that don't cf the case of a submersion. Also, if you have a proper Lie groupoid, its space of objects is foliated by orbits, its quotient space is foliated by conjugation classes of stabilisers etc. You can specify you want the connected components of orbits to be the leaves, but why?
Nov
11
comment When does a leaf space admit a (non-Hausdorff) manifold structure?
Is there something about foliations that demands that leaves are connected? I've noticed this in other papers. Why not just foliate by disconnected manifolds (perhaps not of pure dimension)?
Nov
11
comment What is the relationship between $BU$ and $\textrm{Fred}_0(H)$?
Even better would be: what is a map that makes them homotopy equivalent?
Nov
8
comment Is PA consistent? do we know it?
'Explicit proof of Con(PA) in ZFC'? Do you mean one where all the details in ZFC-language are written out? Or in a proof assistant?