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Scientific events of the Graduiertenkolleg

Event Lecture Series "Triangulated categories of motivic sheaves", 25-28 February 2020, Universität Freiburg (SR 404, Ernst-Zermelo-Str.1, from Feb 25, 2020 10:15 AM to Feb 28, 2020 11:45 AM)
Cohomology theories in algebraic geometry do not come alone, but with associated "sheaf theories" and a rich functoriality with respect to morphisms of schemes ("six operation formalism"). The archetypal example is the theory of étale and l-adic sheaves developed in SGA4-5, which has been adapted to many other settings (analytic sheaves, D-modules, etc.) Thanks to the work of Voevodsky and his successors, we now have a theory of triangulated categories of étale motivic sheaves which generalises the theory of étale sheaves and is, in some sense, the universal such (triangulated) sheaf theory. Surprisingly, morphism groups in these categories are related to algebraic cycles. In this course, I will first explain the construction of these categories and develop their functoriality. I will then describe some of the related conjectures which promise tannakian insights into the structure of algebraic cycles, and I will end with the particular case of 1-motivic sheaves, coming from relative curves, where everything is well-understood.
Event Darmstadt-Erlangen-Freiburg Seminar on Conformal Field theory, Friday, July 5, 2019 Institut für Mathematik Albert-Ludwigs-Universität Freiburg (room 404 of the Mathematics Institute (Ernst-Zermelo-Strasse 1, fourth floor), from Jul 05, 2019 02:00 PM to Jul 05, 2019 06:00 PM)
Event Lecture Series "Hypoelliptic laplacian and applications", 20-24 May 2019, Universität Freiburg (SR 414, Ernst-Zermelo Str.1, from May 20, 2019 09:30 AM to May 24, 2019 12:00 AM)
The purpose of the lectures is to give an introduction to the hypoelliptic Laplacian and to the results which have been obtained so far by this method. The hypoelliptic Laplacian gives a universal interpolation between the Laplacian and the generator of the geodesic flow through a family of hypoelliptic operators acting on a bigger space than the original Laplacian. There are as many hypoelliptic Laplacians as there are Laplacians. To this deformation of operators corresponds an interpolation of dynamics, that interpolates between Brownian motion, with the most irregular paths possible, and the geodesics which have the most regular trajectories. Explicit geometric formulas for certain orbital integrals will appear as consequences. These give in arbitrary dimensions the analogues of the geometric formula obtained by Selberg in the case of Riemann surfaces. The lectures are given by Jean-Michel Bismut. Additionally, he will give a Colloquium talk for the general audience.
Event Fourth Meeting for Young Women in Mathematics “Cohomological Methods in Geometry” (Room 404, Ernst-Zermelo Str.1, from May 01, 2019 05:00 PM to May 03, 2019 03:00 PM)
We are hosting a meeting for young women in mathematics at the University of Freiburg as part of our program "Cohomological Methods in Geometry".
Event Third Meeting for Young Women in Mathematics, February 12-14, 2017 (Room 404, Eckerstraße 1, HS II , from Feb 12, 2017 05:00 PM to Feb 14, 2017 03:00 PM)
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