Sesiones Próximas

Sesiones Anteriores

27 enero 2023
Hora: 08:00 AM
Ponente(s): Joe Rabinoff (Duke U.)
Titulo: Weakly smooth forms and Dolbeault cohomology of curves
Resumen: Gubler and I work out a theory of weakly smooth forms on non-Archimedean analytic spaces closely following the construction of Chambert-Loir and Ducros, but in which harmonic functions are forced to be smooth.  We call such forms "weakly smooth".  We compute the Dolbeault cohomology groups of rig-smooth, compact non-Archimedean curves with respect to this theory, and show that they have the expected dimensions and satisfy Poincaré duality.  We carry out this computation by giving an alternative characterization of weakly smooth forms on curves as pullbacks of certain "smooth forms" on a skeleton of the curve.  This yields an isomorphism between the Dolbeault cohomology of the skeleton, which can be computed using standard combinatorial methods, and the Dolbeault cohomology of the curve.
This work is joint with Walter Gubler.

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13 enero 2023
Hora: 08:00 AM
Ponente(s): Stephen McKean (Harvard U.)
Titulo: Circles of Apollonius two ways
Resumen: There are eight circles tangent to a given trio of circles, provided that one works over the complex numbers. Over the reals, some of these tangent circles can go missing. In order to obtain an invariant count of tangent circles, one needs to count each tangent circle with an appropriate weight. I will talk about two geometric characterizations of such counting weights, as well as how to use these counting weights over any field of characteristic not 2.
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