Geometric Coding Theory
Freitag, 13.11.20, 10:30-11:30, SR 404
I present a geometric approach to error correcting (quantum) codes. \nBy layering hyperbolic surfaces and cyclic codes in the style of a Lasagne I present families of (quantum) codes with best known asymptotic behavior. The ingredients include Coxeter groups, finite groups of Lie type, fiber bundles and a degenerate spectral sequence. \nThis is a joint project with Nikolas Breuckmann (UCL).
Bogomolov's inequality and its applications
Freitag, 20.11.20, 10:30-11:30, SR 404
Bogomolov's inequality is an inequality bounding the degree of the second Chern class of a semistable vector bundle on a smooth algebraic variety. I will talk about various applications of this type of result and its possible possible variants in the Chow ring of the variety.\n
tba
Freitag, 27.11.20, 10:30-11:30, SR 404
Exponential periods and o-minimality
Freitag, 27.11.20, 10:30-11:30, online: lasker
In this talk I will present on joint work with Philipp\nHabegger and Annette Huber. Let α ∈ ℂ be an exponential period. We show\nthat the real and imaginary part of α are up to signs volumes of sets\ndefinable in the o-minimal structure generated by ℚ, the real\nexponential function and sin|_[0,1]. This is a weaker analogue of the\nprecise characterisation of ordinary periods as numbers whose real and\nimaginary part are up to signs volumes of ℚ-semialgebraic sets; and it\npoints to a relation between the theory of periods and o-minimal\nstructures.\n\nFurthermore, we compare the definition of naive exponential periods to\nthe existing definitions of cohomological exponential periods and\nperiods of exponential Nori motives and show that they all lead to the\nsame notion.