Zobrazeno 1 - 10
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pro vyhledávání: '"Brown, Francis"'
We study a closed differential form on the symmetric space of positive definite matrices, which is defined using the Pfaffian and is $\mathsf{GL}_{2n}(\mathbb{Z})$ invariant up to a sign. It gives rise to an infinite family of unstable classes in the
Externí odkaz:
http://arxiv.org/abs/2406.12734
We describe a bigraded cocommutative Hopf algebra structure on the weight zero compactly supported rational cohomology of the moduli space of principally polarized abelian varieties. By relating the primitives for the coproduct to graph cohomology, w
Externí odkaz:
http://arxiv.org/abs/2405.11528
Autor:
Brown, Francis, Schnetz, Oliver
We compute the canonical integrals associated to wheel graphs, and prove that they are proportional to odd zeta values. From this we deduce that wheel classes define explicit non-zero classes in: the locally finite homology of the general linear grou
Externí odkaz:
http://arxiv.org/abs/2402.06757
Autor:
Brown, Francis
We construct bordifications of the moduli spaces of tropical curves and of tropical abelian varieties, and show that the tropical Torelli map extends to their bordifications. We prove that the classical bi-invariant differential forms studied by Cart
Externí odkaz:
http://arxiv.org/abs/2309.12753
Autor:
Brown, Francis, Zudilin, Wadim
We analyse a certain family of cellular integrals, which are period integrals on the moduli space $\mathcal{M}_{0,8}$ of curves of genus zero with eight marked points, which give rise to simultaneous rational approximations to $\zeta(3)$ and $\zeta(5
Externí odkaz:
http://arxiv.org/abs/2210.03391
Autor:
Brown, Francis
To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They are generalised Feynman integrals which satisfy graphical relations obt
Externí odkaz:
http://arxiv.org/abs/2205.10094
Autor:
Brown, Francis
Publikováno v:
SIGMA 17 (2021), 103, 54 pages
We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential forms in q
Externí odkaz:
http://arxiv.org/abs/2101.04419
Autor:
Brown, Francis, Duhr, Claude
Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of dlog-forms with algebraic arguments, which in many cases can be evaluated in terms of multiple polylogarithms. This
Externí odkaz:
http://arxiv.org/abs/2006.09413
Autor:
Brown, Francis, Dupont, Clément
Publikováno v:
Comm. Math. Phys. 382 (2021), 815-874
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of curves of genu
Externí odkaz:
http://arxiv.org/abs/1910.01107