The triply graded link homology - A new approach
Wednesday, 14.10.20, 10:00-11:00, Hörsaal II, Albertstr. 23b
Geometric Coding Theory
Friday, 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
Friday, 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
Friday, 27.11.20, 10:30-11:30, SR 404
Exponential periods and o-minimality
Friday, 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.
Enriques surface fibrations of even index
Friday, 4.12.20, 10:30-11:30, SR 404
..sth around Riemann-Zariski space of valuations
Friday, 11.12.20, 10:30-11:30, SR 404
o-minimal homotopy theory
Friday, 18.12.20, 10:30-11:30, SR 404
S-unit equation and Chabauty
Friday, 8.1.21, 10:30-11:30, SR 404
Algebraic cycles and refined unramified cohomology
Friday, 15.1.21, 10:30-11:30, SR 404
We introduce refined unramified cohomology groups. This notion allows us to give in arbitrary degree a cohomological interpretation of the failure of integral Hodge- or Tate-type conjectures, of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion classes with trivial transcendental Abel--Jacobi invariant. Our approach simplifies and generalizes to cycles of arbitrary codimension previous results of Bloch--Ogus, Colliot-Thélène--Voisin, Voisin, and Ma that concerned cycles of codimension two or three. As an application, we give for any i>2 the first example of a uniruled smooth complex projective variety for which the integral Hodge conjecture fails for codimension i-cycles in a way that cannot be explained by the failure on any lower-dimensional variety.
Irregular fibrations and derived categories
Friday, 22.1.21, 10:30-11:30, SR 404
In this seminar I will show that an equivalence of derived categories of sheaves of smooth projective varieties preserves some specific classes of fibrations over varieties of maximal Albanese dimension. These types of fibrations, called chi-positive higher irrational pencils, can be thought as an extension to higher-dimension of the notion of a irrational pencil over a smooth curve of genus greater or equal to two. This is a joint work with F. Caucci and G. Pareschi.
Cone structures and parabolic geometries
Friday, 29.1.21, 10:30-11:30, SR 404
tba
Friday, 5.2.21, 10:30-11:30, SR 404
Complex rank 3 vector bundles on CP^5
Friday, 12.2.21, 15:00-16:00, zoom
Given the ubiquity of vector bundles, it is perhaps\nsurprising that there are so many open questions about them -- even on\nprojective spaces. In this talk, I will outline some results about\nvector bundles on projective spaces, including my ongoing work on\ncomplex rank 3 topological vector bundles on CP^5. In particular, I\nwill describe a classification of topological bundles which involves a\nsurprising connection to topological modular forms; a concrete,\nrank-preserving additive structure which allows for the construction of\nnew rank 3 bundles on CP^5 from "simple" ones; and future directions\nrelated to this project, including questions I have about how to make\nthis picture more "algebraic".\n