arXiv subjects

Cameron James Deverall Kemp

Publications and source records attributed to Cameron James Deverall Kemp.

3 recordsLinked to original sources

arXiv2026

Relations between multiple zeta values and delta values from Drinfeld's associator series

It is shown that novel relations between multiple zeta values and single-variable multiple polylogarithms at 1/2 (delta values) can be derived by comparing two distinct, yet a priori equal, series formulae for the Drinfeld associator (from the Knizhnik-Zamolodchikov connection). In particular, we demonstrate that two new relations are found by comparing the fifth order terms of each series formula.

math.NT↗

arXiv2025

Cartier integration of infinitesimal 2-braidings via 2-holonomy of the CMKZ 2-connection, I: Hexagonators and the Breen polytope

This paper follows on from "Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings". Given a symmetric strict infinitesimal 2-braiding on a symmetric strict monoidal cochain 2-category, we construct a candidate hexagonator series as a 2-holonomy with respect to the Cirio-Martins-Knizhnik-Zamolodchikov (CMKZ) fake flat 2-connection over the configuration space of 3 distinguishable particles on the complex line, $Y_3$. The second-order term of the hexagonator series is computed and found to agree with the "infinitesimal hexagonator" from the aforementioned work. Finally, we assume a coherent totally symmetric strict infinitesimal 2-braiding and prove that the Breen polytope axiom is satisfied by translating it into a 2-loop in $Y_3$.

math.QA↗

arXiv2025

Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings

This paper follows on from ``Infinitesimal 2-braidings from 2-shifted Poisson structures". It is demonstrated that the hexagonators appearing at second order satisfy the requisite axioms of a braided monoidal cochain 2-category provided that the strict infinitesimal 2-braiding is totally symmetric and coherent (in Cirio and Faria Martins' sense). We show that those infinitesimal 2-braidings induced by 2-shifted Poisson structures are indeed totally symmetric and we relate coherency to the third-weight component of the Maurer-Cartan equation that a 2-shifted Poisson structure must satisfy. Furthermore, we show that 3-shifted Poisson structures and ``coboundary" 2-shifted Poisson structures induce syllepses.

math.QA↗