Birational geometry of foliations
Friday, 2.7.21, 10:30-11:30, virtueller Raum Lasker
I will try to explain, by means of some examples and recent results, how the classical framework of the Minimal Model Program has been extended to the case of foliation, in particular in low dimension, as well as, how it has been used to initiate a systematic study and classification of foliations from a birational view point. \nThe talk will feature joint work with C. Spicer.
Frobenius kernels for automorphism group schemes
Friday, 9.7.21, 10:30-11:30, virtueller Raum Lasker
We establish structure results for Frobenius kernels of automorphism group schemes for surfaces of general type in positive characteristics. It turns out that there are surprisingly few possibilities. This relies on properties of the famous Witt algebra, a simple Lie algebra without finite-dimensional counterpart over the complex numbers, together with is twisted forms. The result actually holds true for rather general schemes, under the assumption that the Frobenius kernel has large isotropy group at the generic point. This is joint work with Nikolaos Tziolas.\n
Cohen-Lenstra-Martinet heuristics on class groups of number fields
Friday, 16.7.21, 10:30-11:30, virtueller Raum Lasker
In the 1980s Cohen and Lenstra proposed a probabilistic model\nfor the behaviour of class groups of quadratic number fields. A few\nyears later, it was generalised by Cohen and Martinet to class groups\nof more general families of number fields. Recently, in joint work with\nLenstra we disproved these conjectures -- in two completely different\nways, and in joint work with Lenstra and Johnston we have offered a\ncorrected version. In my talk I will give an overview of this work.
The effective model structure and infinity-groupoid objects
Friday, 23.7.21, 10:30-11:30, virtueller Raum Lasker
I will discuss a construction of a new model structure on\nsimplicial objects in a countably lextensive category (i.e., a category\nwith well behaved finite limits and countable coproducts). This builds\non previous work on a constructive model structure on simplicial sets,\noriginally motivated by modelling Homotopy Type Theory, but now\napplicable in a much wider context. This is joint work with Nicola\nGambino, Simon Henry and Christian Sattler.\n