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I am a postdoc in maths with a degree in theoretical physics. I am interested in mathematical structures in quantum field theory and string theory, see here.

4h
awarded  Announcer
14h
comment Extended TFT with coefficients in spans in any $\infty$-topos
I should maybe say that the idea would be to use naturality of the equivalences in the case of $\infty$-groupoids to reduce the desired equivalence in the case of general $\mathbf{H}$ to a presheaf of equivalences and then conclude from that.
2d
asked Extended TFT with coefficients in spans in any $\infty$-topos
Oct
15
comment “extended TQFT” versus “TQFT with defects”
Yes, representations of cobordisms with singularities encode TFTs with boundaries and defects. For "pre-quantum" field theory this is discussed in sections 3.9.14.4 to 3.9.14.6 of arxiv.org/abs/1310.7930 (improved version in preparation at ncatlab.org/schreiber/show/Local+prequantum+field+theory). For quantization of this: arxiv.org/abs/1402.7041 . This is based on discussion with Domenico Fiorenza and Alessandro Valentino that recently appeared as arxiv.org/abs/1409.5723
Oct
15
awarded  Yearling
Oct
13
awarded  Announcer
Sep
24
awarded  Autobiographer
Sep
15
comment From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?
Chris Schommer-Pries has kindly pointed out that there should be a positive answer to the second of my questions: the projectively flat Hitchin connection on the Riemann moduli space canonically lifts to a genuinely flat connection on the 3-framing moduli space. This follows with a) Segal's deprojectivization, 2) the fact that "Atiyah 2-framings" provide "level-12 riggings" and 3) the observation (which Chris kindly highlighted) that there is a canonical functor from the 1-type of 3-framings to that of "Atiyah 2-framings" (see ncatlab.org/nlab/show/modular+functor#TopologicalLift).
Sep
11
reviewed Approve suggested edit on homotopy exact sequence for the étale fundamental group
Sep
10
comment When does a moduli space admit a spin structure?
There are of course moduli spaces which are both important and at the same time are geometrically simple, a key example being the (higher) Jacobians ncatlab.org/nlab/show/intermediate+Jacobian which are simply higher dimensional tori. Hence these even admit a framing and in particular admit whatever G-structure you want.
Sep
10
revised From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?
fixed trivial typos
Sep
10
revised From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?
added 2 characters in body
Sep
10
asked From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?
Sep
9
comment Gauge-theoretic formulation of Maxwell equations
...apart from that saying that the EM-field is a U(1)-principal connection is part of mathematical theory building in physics and not something one may derive from first principles. (Well, one may give some general arguments about the need for gauge fields to be modeled in differential cohomology, but I guess that's not what you are after.)
Sep
9
comment Gauge-theoretic formulation of Maxwell equations
Could you say what exactly you would want to see proven? There is the original Maxwell's equations from the 1850s not nvolving any principal bundles. Then there is Dirac's charge quantization argument from the 1930s which argues that this needs to be refined to the version where the electromagnetic field is a connection on a principal bundle. What one may derive is that this is the right structure to produce U(1)-valued line holonomies, which are the gauge coupling action functionals of charged particles (electrons). But apart from that...
Sep
7
comment Algebraic K-theory and Homotopy Sheaves
Thanks, Adeel, this is good. Have added these references here: ncatlab.org/nlab/show/algebraic+K-theory#Descent
Sep
4
reviewed Approve suggested edit on Generalization of the equilateral triangle?
Sep
4
answered Algebraic K-theory and Homotopy Sheaves
Aug
31
awarded  Announcer
Aug
29
comment Does the notion of a “coherent state” exist in TQFTs? (ETQFTs?)
Maybe one should amplify that such definitions (ncatlab.org/nlab/show/coherent+state+in+geometric+quantization) hence depend on having "pre-quantum" data (often called "classical" data). If you instead have a quantizED field theory without the information of how it came about from quantizATION, say a TQFT or ETQFT given by (just) a functor/n-functor, then these definitions of coherent state won't apply.