Minimal surfaces, flat cone spheres and moduli spaces of staircases

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

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On the Voevodsky motive of the moduli space of Higgs bundles on a curve

Selecta Mathematica ◽

10.1007/s00029-020-00610-5 ◽

2021 ◽

Vol 27 (1) ◽

Author(s):

Victoria Hoskins ◽

Simon Pepin Lehalleur

Keyword(s):

Moduli Space ◽

Moduli Spaces ◽

Characteristic Zero ◽

Rational Point ◽

Triangulated Category ◽

Higgs Bundles ◽

Projective Curve ◽

Smooth Projective Curve ◽

De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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On different notions of calibrations for minimal partitions and minimal networks in ℝ2

Advances in Calculus of Variations ◽

10.1515/acv-2019-0005 ◽

2019 ◽

Vol 0 (0) ◽

Author(s):

Marcello Carioni ◽

Alessandra Pluda

Keyword(s):

Minimal Surfaces ◽

Steiner Problem ◽

Minimal Networks

Abstract Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of the Steiner problem in several variants. Our goal is to compare the different notions of calibrations for the Steiner problem and for planar minimal partitions that are already present in the literature. The paper is then complemented with remarks on the convexification of the problem, on nonexistence of calibrations and on calibrations in families.

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