RESEARCH IN PAIRS
NonArchimedean Methods in Lipschitz Geometry (2573)
Méthodes nonarchimédiennes en géométrie de Lipschitz
Dates: 1223 July 2021
Place: CIRM (Marseille Luminy, France)
NonArchimedean Methods in Lipschitz Geometry (2573)
Méthodes nonarchimédiennes en géométrie de Lipschitz
Dates: 1223 July 2021
Place: CIRM (Marseille Luminy, France)
DESCRIPTION
The nonarchimedean viewpoint to geometry has already started pervading Lipschitz and metric geometry in several directions. But a lot remains to be done in this direction, such as the adaptation of Moderately Discontinuous Homology [2] to the nonarchimedean setting, the extension of the Laplacian formula on inner rates [1] to other functions, for instance the outer rate functions associated to outer metric for surface singularities and their extension to the higher dimensional case, and the probable central role played by ultrametrics on nonarchimedean links whose study is pioneered in the series of work by Garcia Barroso, Gonzalez Perez, Ruggiero and PopescuPampu [4, 5, 6, 7].
The aim of this Research in Pairs is to advance towards the construction of Lipschitz or metric invariants based on the nonarchimedean viewpoint. 
PARTICIPANTS

References
[1] André Belotto, Lorenzo Fantini, Anne Pichon, Inner geometry of complex surfaces: a valuative approach, (2019) 42 pages, arXiv:1905.01677.
[2] J. Fernandez de Bobadilla, Sonja Heinze, Maria Pe Pereira, Jose Edson Sampaio, Moderately Discontinuous Homology, (2019) 65 pages, arXiv:1910.12552.
[3] J. Fernandez de Bobadilla, M. Pe Pereira, P. PopescuPampu, On the generalized Nash problem for smooth germs and adjacencies of curve singularities, Adv. Math. 320 (2017), 12691317.
[4] E. R. Garcia Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, Ultrametric spaces of branches on arborescent singularities. In Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday, pages 55–106. Springer, 2018.
[5] E. R. Garcıa Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, The valuative tree is the projective limit of EggersWall trees. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113(4):4051–4105, 2019.
[6] E. R. Garcia Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, M. Ruggiero. Ultrametric properties for valuation spaces of normal surface singularities. Trans. Amer. Math. Soc., 372(12):8423–8475, 2019.
[7] E. R. Garcıa Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, The combinatorics of plane curve singularities. how Newton polygons blossom into lotuses. Preprint.
[1] André Belotto, Lorenzo Fantini, Anne Pichon, Inner geometry of complex surfaces: a valuative approach, (2019) 42 pages, arXiv:1905.01677.
[2] J. Fernandez de Bobadilla, Sonja Heinze, Maria Pe Pereira, Jose Edson Sampaio, Moderately Discontinuous Homology, (2019) 65 pages, arXiv:1910.12552.
[3] J. Fernandez de Bobadilla, M. Pe Pereira, P. PopescuPampu, On the generalized Nash problem for smooth germs and adjacencies of curve singularities, Adv. Math. 320 (2017), 12691317.
[4] E. R. Garcia Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, Ultrametric spaces of branches on arborescent singularities. In Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday, pages 55–106. Springer, 2018.
[5] E. R. Garcıa Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, The valuative tree is the projective limit of EggersWall trees. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113(4):4051–4105, 2019.
[6] E. R. Garcia Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, M. Ruggiero. Ultrametric properties for valuation spaces of normal surface singularities. Trans. Amer. Math. Soc., 372(12):8423–8475, 2019.
[7] E. R. Garcıa Barroso, P. D. Gonzalez Perez, and P. PopescuPampu, The combinatorics of plane curve singularities. how Newton polygons blossom into lotuses. Preprint.
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