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I am a postdoc in mathematics, but have my degree in theoretical physics. My work is about mathematical structures motivated from quantum field theory and string theory. For more see my personal web on the nLab.


Jan
11
comment How to treat differentials and infinitesimals?
On the other hand one can choose to build concrete models for the axioms in which notably the textbooks by Kock are written, hence for toposes that validate the Kock-Lawvere axioms. In the typical such models the category of smooth manifolds is enlarged somewhat by objects known as "smooth loci", which include for instance the space formally dual to the "ring of dual numbers", which is just the ring embodying the equation "epsilon^2 = 0". This more concrete incarnation of SDG can be phrased entirely in classical logic and hence shows which classical notions embody the idea of infinitesimals.
Jan
11
comment How to treat differentials and infinitesimals?
There are two complementary aspects to this. On the one hand the categorical logic of toposes allows to formally speak of the subset of the real line of elements that square to 0. This is just what people following Leibniz intuitively did anyway, but categorical logic shows that and how exactly this is consistent. This is then how notably Anders Kock (home.imf.au.dk/kock) wrote his two textbooks on synthetic differential geometry (home.imf.au.dk/kock/SGM-final.pdf): he speaks "synthetically" of the subset D of R on the elements that square to 0 and derives all of diff geometry.
Jan
9
comment What are the practical applications of quantum foundations?
Yes, I agree, one needs to be careful and I think the main message is that it is good to keep an open mind, either way. As in the last sentence of the quote above: "So it is a problem whether or not to worry about philosophies behind ideas"
Jan
9
awarded  Announcer
Jan
9
awarded  Nice Answer
Jan
9
revised How to treat differentials and infinitesimals?
deleted 34 characters in body
Jan
9
revised How to treat differentials and infinitesimals?
added 12 characters in body
Jan
9
answered How to treat differentials and infinitesimals?
Jan
7
answered What are the practical applications of quantum foundations?
Dec
29
awarded  Good Answer
Dec
25
comment Is it expected that all stellar black holes will be spinning near the maximum allowed $\omega$-velocity?
Nice comment, but for emphasis, let's notice that this is an argument in favor of the answer "yes, black holes will tend to have maximum angular momentum". Because that maximum angular momentum ("extremal Kerr black hole") is J=M^2, hence q=1. So under black hole formation a star may generally have more than this critical angular momentum and black hole formation sets in right at the critical value.
Dec
11
comment Why aren't we Boltzmann brains in an infinite universe?
-1 for using the words "strong argument" in this context. All this is intellectually undisciplined speculation without any attempt to base arguments on science or logic.
Nov
26
awarded  Enlightened
Nov
20
answered If space and time are equivalent, what's Spin in time dimension
Nov
16
awarded  Announcer
Nov
15
answered Etale bundles and sheaves
Nov
15
revised SUSY's Critical role in String Theory
fixed a link
Nov
15
answered SUSY's Critical role in String Theory
Nov
13
awarded  Nice Answer
Nov
10
comment How algebraic geometry and motives appears in physics?
For the appearance of motivic Galois groups in perturbative quantization see Connes-Marcolli's textbook ncatlab.org/nlab/show/… . For the appearance of generalized pure motives in higher geometric quantization see this thesis: ncatlab.org/schreiber/show/master+thesis+Nuiten .