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Seminários, para a disseminação informal de resultados de investigação, trabalho exploratório de equipas de investigação, actividades de difusão, etc., constituem a forma mais simples de encontros num centro de investigação de matemática.

O CAMGSD regista e publica o calendário dos seus seminários há bastante tempo, servindo páginas como esta não só como um método de anúncio dessas actividades mas também como um registo histórico.

Para uma interface de busca completa ver a página de seminários do Departamento de Matemática.

Sala P3.10, Pavilhão de Matemática Instituto Superior Técnico https://tecnico.ulisboa.pt

Geometria em Lisboa

Ana Rita Pires, University of Edinburgh.

The symplectic version of the problem of packing K balls into a ball in the densest way possible (in 4 dimensions) can be extended to that of symplectically embedding an ellipsoid into a ball as small as possible. A classic result due to McDuff and Schlenk asserts that the function that encodes this problem has a remarkable structure: its graph has infinitely many corners, determined by Fibonacci numbers, that fit together to form an infinite staircase.

This ellipsoid embedding function can be equally defined for other targets, and this talk will be about other targets for which the function has and does not have an infinite staircase. Firstly we will see how in the case when these targets have lattice moment polygons, the targets with infinite staircases seem to be exactly those whose polygon is reflexive (i.e., has one interior lattice point). Secondly, we will look at the family of one-point blowups of $CP^2$, where the answer involves self-similar behaviour akin to the Cantor set.

This talk is based on various projects, joint with Dan Cristofaro-Gardiner, Tara Holm, Alessia Mandini, Maria Bertozzi, Tara Holm, Emily Maw, Dusa McDuff, Grace Mwakyoma, Morgan Weiler, and Nicki Magill.

Financiamento actual: FCT UIDB/04459/2020 & FCT UIDP/04459/2020.

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