Weekend research talk: Taylor Dupuy on Deninger's RH proof strategy

One of the dreams related to the Generalized Riemann Hypothesis is that the zeros of an L-function might have a spectral interpretation, i.e. they might be eigenvalues of some operator, or at least closely related to such eigenvalues.

Since there are infinitely many nontrivial zeros, the operator seemingly would have to act on an infinite-dimensional space, perhaps a Hilbert space. Based on the Rosetta Stone analogy, this space might be constructed as a cohomology group of some underlying $\mathbb{F}_1$-geometric object. All of this is speculative. But I'd like to share a well-hidden YouTube gem, in which Taylor Dupuy walks us through the proof of the Riemann Hypothesis proof by Deninger, which relies on a hypothetical spectral framework of this kind, involving a conjectural cohomology theory and something called a Hodge star operator. This is a great watch. The proof itself appears in the last seven minutes of the video, from 25:35.

Note that the video is the final instalment of a 6-episode mini-course on RH which you might find interesting in its entirety, and also that Dupuy has lots of other cool videos on his channel, like this introduction to the abc conjecture.

Tomorrow I'll be posting the next chapter of the RH Saga course notes, where we'll see some of the connections to random matrix models that have been viewed for a long time as partial evidence towards a spectral interpretation.