# Felix Klein Lectures 2022

## Jacob Lurie (Institute for Advanced Studies, Princeton)

Dates:

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

### Abstract:

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 $\mathscr{D}_{X}$-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).

If you are interested in participating, please use the online application platform