Author Archives: Persiflage

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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Artin No-Go Lemma

Posted on December 13, 2016 by Persiflage

The problem of constructing Galois representations associated to Maass forms with eigenvalue 1/4 is, by now, a fairly notorious problem. The only known strategy, first explained by Carayol, is to first transfer the representation to a unitary group over an … Continue reading →

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Z_p-extensions of Number Fields, Part II

Posted on November 26, 2016 by Persiflage

This is continuation of the last post. We claimed there that we were going to deform a totally real number field of degree n into a field with signature (r,s) with r+2s = n, and pass information about Leopoldt’s conjecture … Continue reading →

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Z_p-extensions of Number Fields, Part I

Posted on November 23, 2016 by Persiflage

In the next few posts, I want to discuss a problem that came up when I wrote a paper with Barry Mazur. We had a few observations and remarks that we discussed as part of a possible sequel but which … Continue reading →

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Coffee Passport

Posted on October 24, 2016 by Persiflage

Having completed my visits to 22 Chicago coffee shops on the Chicago indie coffee passport tour, here are my notes together with a (rough) ranking in four categories from best to worst, taking into account a number of factors, including … Continue reading →

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