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Felix Klein Lectures 2022 with Jacob Lurie

Posted in
Tue, 15/11/2022 - 12:00 - 13:00
MPIM Lecture Hall

Felix Klein Lectures 2022

organised by the HCM. Please find the official website of the event here.

A Riemann-Hilbert Correspondence in p-adic Geometry

Jacob Lurie (Institute for Advanced Studies, Princeton)


Lecture 1: MPI, Tuesday, Nov 15, 12:00--13:00;
Lecture 2: MPI, Thursday, Nov 17, 14:00--15:00;
Lecture 3: MPI, Tuesday, Nov 22, 16:30--17:30;
Lecture 4: MPI, Thursday, Nov 24, 14:00--15:00;
Lecture 5: MPI, Tuesday, Nov 29, 16:30--17:30;
Lecture 6: MPI, Thursday, Dec 1, 14:00--15:00.

Venue: MPIM lecture hall

Members of the Bonn mathematics community do not have to apply for participation via this platform. Access to the lecture hall will be granted to them on a first come first served basis until all available seats are taken. The registration for external people is already closed.


At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic differential equations. A central result is the celebrated Riemann-Hilbert correspondence of Kashiwara and Mebkhout, which supplies a fully faithful embedding from the category of perverse sheaves on $X$ to the category of algebraic $\mathfrak{D}_X$-modules. This embedding is transcendental in nature: that is, it depends essentially on the (archimedean) topology of the field of complex numbers. It is natural to ask if there is some counterpart of the Riemann-Hilbert correspondence over nonarchimedean fields, such as the field $\mathbf{Q}_p$ of $p$-adic rational numbers. In this series of lectures, I will survey some of what is known about this question and describe some recent progress, using tools from the theory of prismatic cohomology (joint work with Bhargav Bhatt).

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