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December 14, 2020 / Samuel Grushevsky (Stony Brook Univ.) = = Differentials on Riemann surfaces and the geometry of the moduli spaces of curves |
January 25, 2021
Alexander Bobenko (Inst. Mathematik, TU Berlin)
On a discretization of confocal quadrics: Geometric parametrizations, integrable systems and incircular nets
We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system may be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics. The theory is illustrated with a variety of examples in two and three dimensions. These include confocal coordinate systems parametrized in terms of Jacobi elliptic functions. Connections with incircular nets and elliptic billiards are established
February 1, 2021
Andrei Smilga (Subatech, Univ. de Nantes)
Spin(7) instantons in eight dimensions
We explicitly construct topologically nontrivial 8-dimensional gauge field configurations that belong to the algebra $spin(7)$ and are associated with the homotopy group $\pi_7[Spin(7)] = \mathbb{Z}$