12,259 reputation
437112
bio website ncatlab.org/nlab/show/…
location Adelaide, Australia
age 31
visits member for 5 years, 9 months
seen 6 hours ago

Pure mathematician interested in category theory and foundations.


13h
comment Why should we care about “higher infinities” outside of set theory?
Wooden -> Woodin
2d
comment Which Lie algebra admit symplectic forms
Welcome to MO, Wolfgang!
2d
comment Why should we care about “higher infinities” outside of set theory?
You may also be interested in predicative mathematics: ncatlab.org/nlab/show/predicative+mathematics. It doesn't get rid of higher cardinalities, insomuch as this still makes sense, but does reject the notion of power set (still keeping, for instance, function sets more generally, but rejecting a subobject classfying set, which is classical mathematics is {0,1})
2d
comment Geodesics on SO(3)
principle -> principal
2d
comment Why should we care about “higher infinities” outside of set theory?
You may be interested in a foundation where one can form each of the finitely iterated power sets $P^n(\mathbb{N})$, but draw no conclusion about anything bigger. Then one is assured of having spaces of functions that turn up in analysis etc, starting from existing sets. See: arxiv.org/abs/1212.6543, and this question, phrased in terms of higher cardinalities arising from Replacement: mathoverflow.net/questions/208711/who-needs-replacement-anyway
2d
comment How to rewrite square root without exponents?
No${}{}{}{}{}{}$
2d
comment Why should we care about “higher infinities” outside of set theory?
What's the cardinality of the space of operators on a separable Banach space?
2d
comment Detecting torsion-classified bundles by differential invariants
The above assumes that one can find a section of P over an open set with complement of zero measure, so that the integral can be done.
Aug
26
comment Detecting torsion-classified bundles by differential invariants
The question in a nutshell is this: can I calculate a number from a connection that tells me about the classification of the underlying bundle by 'torsion' invariants?
Aug
26
awarded  Good Question
Aug
26
comment How much of the ATLAS of finite groups is independently checked and/or computer verified?
Do you know any specific examples where there are no other sources to corroborate facts stated in the ATLAS?
Aug
26
revised Detecting torsion-classified bundles by differential invariants
added 72 characters in body
Aug
26
asked Detecting torsion-classified bundles by differential invariants
Aug
26
comment Representation ring of circle group over complex field
I suggest this question would be a better fit at math.stackexchange.com - here it's gathering votes to close.
Aug
26
awarded  Popular Question
Aug
26
revised How much of the ATLAS of finite groups is independently checked and/or computer verified?
Clarified question
Aug
24
comment Soft Question: Relationships Between Moduli Space and Objects They Parametrize
Another example to keep in mind is the work of Mirzakhani, where dynamics on moduli spaces of Riemann surfaces tell us something about Riemann surfaces themselves. See eg mathoverflow.net/questions/199212/maryam-mirzakhanis-works
Aug
24
comment How to compute (co)limits of enriched categories?
@user40276 for future reference, anything four years old or older on ScienceDirect in most if not all pure mathematics journals is free to read. Part of Elsevier trying to win back the hearts of mathematicians (you'll notice it's not true for as many journal in other fields, like theoretical physics, that have similar half-life for their papers).
Aug
24
comment Probability and Statistics
Wrong website! Have a read of some other questions here...
Aug
21
awarded  Popular Question