Author Archives: Persiflage

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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Serre 1: Calegari 0

Posted on October 18, 2016 by Persiflage

I just spent a week or so trying to determine whether Serre’s conjecture about the congruence subgroup property was false for a very specific class of S-arithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading →

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Champagne Marxists

Posted on October 15, 2016 by Persiflage

One wonders whether it is only the US in which highly educated white liberal college students from the upper reaches of the socio-economic strata support the extremely regressive Bernie Sanders-style policy of spending a trillion dollars on free education for … Continue reading →

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Sawada Coffee

Posted on August 23, 2016 by Persiflage

The Tip: I received a hot tip to visit Sawada Coffee, proclaimed (by a facebook friend of my source) as “the best coffee in Chicago.” Here is a review. First impressions: Somewhat of a skater-hipster vibe. It turned out that Sawada … Continue reading →

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fivethirtyeight.com doesn’t understand mathematics

Posted on June 2, 2016 by Persiflage

I happened to find myself browsing fivethirtyeight.com a few weeks ago, where I came across a column known as the “riddler.” The particular problem of the week (see here) was to answer the following: Problem: It’s Friday and that means … Continue reading →

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Prime divisors of polynomials

Posted on May 29, 2016 by Persiflage

A heuristic model from the last post suggests that the “expected” order of the Galois group associated to a weight one modular form of projective type \(A_5\) is infinite. And when one tries to solve the inverse Galois problem for … Continue reading →

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Central Extensions and Weight One Forms

Posted on May 23, 2016 by Persiflage

As mentioned in the comments to the last post, Kevin Buzzard and Alan Lauder have made an extensive computation of weight one modular forms in characteristic zero (see also here). Thinking about what that data might contain, I wondered about … Continue reading →

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