Symmetries

By Hugo Bacard. 2014

459 citations recorded by the source corpus.

Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be explained. One way to do this is to embed sets to higher categories and especially into higher groupoids as already envisioned by Grothendieck, and more recently by Voevodsky. We simply outline this idea in these notes.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d2e5e714b59d5be80522c8013088dcc0e35c9958

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In Statistical and Nonlinear Physics

Citations in the corpus

Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations (2015, background): “However, outer automorphism groups for reductive Lie algebras are relatively small and gauging them can reduce the rank of F but not freeze it completely [43].”
Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, background): “In such situation, it is also known that all such Fanos admit KE metrics [4].”
Dispersion-managed solitons in fibre systems and lasers (2012, background): “oscillations of the pulse parameter for various transmission systems, away from the lossless limit (LDM ∼ LA) [140,143,157, 158].”
Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties (2011, methodology): “Inspired by a nice construction of [1], we prove a criterion that produces a rather broad class of log Fano pairs having a proper Mabuchi functional.”