Termine

Abstract: In this talk, I will present a construction of new SU(2)-invariant complete negative Einstein metrics on the complex line bundle O(-4) over CP^1. The metrics are conformally compact and generically neither Kähler nor self-dual. The proof involves using rigorous numerical techniques (Chebyshev polynomials and arbitrary-precision interval arithmetic) to produce an approximate Einstein metric in a bounded region near the singular orbit, then perturbing it to a genuine Einstein metric using fixed-point methods. At the boundary of this region, we show that the latter metric is sufficiently close to hyperbolic space so that it extends to a complete, asymptotically hyperbolic Einstein metric. Our construction is based on previous work of Buttsworth?Hodgkinson.

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.

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Further information

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