Author Archives: Persiflage

Erdős Number 3!

Posted on March 26, 2017 by Persiflage

My chances at this point of writing a paper with Erdős are probably very small. My chances of writing a paper with one of Erdős’ collaborators is also quite small. I had assumed that I had not even met — … Continue reading →

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Film Criticism

Posted on March 22, 2017 by Persiflage

You know that feeling you get when you want to understand the precise conjectural relationship between the cohomology of arithmetic varieties and Galois representations? I finally get it. Du musst Caligari werden! Oh, and if you think I’m crazy, it’s … Continue reading →

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A non-liftable weight one form modulo p^2

Posted on March 10, 2017 by Persiflage

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: \(\rho: \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \rightarrow \mathrm{GL}_2(\mathbf{Z}/p^2 \mathbf{Z})\) which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). … Continue reading →

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Report from MSRI and Berkeley

Posted on March 7, 2017 by Persiflage

Having attended last Friday’s academic sponsors’ day at MSRI, I can provide a little more context concerning the issues expressed last time. But first, it’s time for the current edition of NAME AND SHAME: There are currently 105 universities which … Continue reading →

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Complain about MSRI day

Posted on February 28, 2017 by Persiflage

I will be heading off later this week to the Academic Sponsors’ Day at MSRI, going as Shmuel’s proxy for uchicago. I’m not sure to what extent (if any) there is for me to make policy suggestions, but any comments … Continue reading →

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Virtual coherent cohomology

Posted on February 22, 2017 by Persiflage

I gave a talk yesterday where I attempted to draw parallels between the cohomology of (arithmetic) 3-manifolds and weight one modular forms. It was natural then to think about whether there was an analogue of the virtual Betti number conjecture. … Continue reading →

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The class number 100 problem

Posted on January 19, 2017 by Persiflage

Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading →

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Central Extensions, Updated

Posted on January 15, 2017 by Persiflage

I previously mentioned a problem concerning polynomials, whose motivation came from thinking about weight one forms and the inverse Galois problem for finite subgroups of \(\mathrm{GL}_2(\mathbf{C}).\) I still like the polynomial problem, but I realized that I was confused about … Continue reading →

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Correspondance Serre-Tate, Part I

Posted on December 24, 2016 by Persiflage

Reading the correspondence between Serre and Tate has been as delightful as one could expect. What is very nice to see — although perhaps not so surprising — is the utter delight that both Serre and Tate find in discussing … Continue reading →

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Indulgences

Posted on December 15, 2016 by Persiflage

Today is Persiflage’s birthday, but let us not also forget to wish many happy returns to friends of the blog Ana and Vytas, who share the same birthday! Here is how I plan to celebrate: I will spare you with the … Continue reading →

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