Termine

The talk is based on joint work with Matt Durham and Yair Minsky where we construct metrics that satisfy a CAT(0)-like inequality involving a sublinear error for a large class of groups including mapping class groups and a lot of their quotients, most 3-manifold groups, extra-large Artin groups, extension of Veech groups and multicurve stabilisers, and many others. These metrics in turn allow one to construct contractible Rips complexes with "nice" compactifications, and to use those to show that the groups in our large class satisfy the Farrell-Jones conjecture.

Abstract: In this talk, I will explain a log-perfectoid toric mirror symmetry that compares certain almost quasi-coherent sheaves categories and topologicial sheaf categories with microlocal condition. The 1-dimension statement already has interesting applications in irregular Riemann-Hilbert correspondence and quantitative symplectic geometry. This talk is based on a joint work with Tatsuki Kuwagaki.

The Prym varieties introduced by Mumford in the 70's opened new perspectives in the study of the moduli space of abelian varieties: Prym varieties are abelian varieties arising from covers between curves. They generalize Jacobians and provide a larger class of abelian varieties which can be understood in terms of 1-dimensional geometric objects. For instance, it is known that the general principally polarized abelian variety of dimension less than or equal to 5 is the Prym variety of some unramified double cover. The Prym map between the moduli space of covers and the moduli space of abelian varieties assigns to each covering its Prym variety. In this talk I will discuss the geometry of the fibres of the Prym map for double covers in low genera, the global injectivity of the Prym map for ramified double covers, as well as the most recent results on the general injectivity of the Prym map for cyclic covers.

Further information

Further information

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