Author Archives: Persiflage

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Posted on August 19, 2021 by Persiflage

The target audience of this blog (especially the mathematics) is usually professional mathematicians in the Langlands program. I do sometimes, however, have posts suitable for a broader mathematical audience. Very rarely though do I have anything (possibly) interesting to say … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , | 14 Comments

Divisors near sqrt(n)

Posted on June 8, 2021 by Persiflage

Analytic Number Theory Alert! An even more idle question than normal (that’s because it comes from twitter). Alex Kontorovich noted with pleasure the following pictorial representation of the integers from a Veritasium youtube video, where prime numbers are represented by … Continue reading →

Posted in Mathematics | Tagged , , , | 5 Comments

Potential Automorphy for GL(n)

Posted on April 29, 2021 by Persiflage

Fresh on the arXiv, a nice new paper by Lie Qian proving potential automorphy results for ordinary Galois representations \(\rho: G_F \rightarrow \mathrm{GL}_n(\mathbf{Q}_p)\) of regular weight \([0,1,\ldots,n-1]\) for arbitrary CM fields \(F\). The key step in light of the 10-author … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Don’t cite my paper!

Posted on April 26, 2021 by Persiflage

The process of publishing a paper is an extremely long one, and it is not atypical to take several years from the first submission to the paper finally being accepted. The one part of the process that happens extremely quickly, … Continue reading →

Posted in Rant | Tagged , , | 18 Comments

The Arbeitsgemeinschaft has returned!

Posted on March 26, 2021 by Persiflage

An update on this post; the Arbeitsgemeinschaft on derived Galois deformation rings and the cohomology of arithmetic groups will now be taking place the week of April 5th. Here is some practical information if you are curious. Is there somewhere … Continue reading →

Posted in Mathematics | Tagged , , | 2 Comments

Test Your Intuition: p-adic local Langlands edition

Posted on March 9, 2021 by Persiflage

Taking a page from Gil Kalai, here is a question to test your intuition about 2-dimensional crystalline deformation rings. Fix a representation: \(\rho: G_{\mathbf{Q}_p} \rightarrow \mathrm{GL}_2(\overline{\mathbf{F}}_p)\) after twisting, let me assume that this representation has a crystalline lift of weight … Continue reading →

Posted in Mathematics | Tagged , , | 12 Comments

Fermat Challenge

Posted on February 21, 2021 by Persiflage

A challenge inspired from a question of Doron Zeilberger. Do there exist arbitrarily large integers \(n\) with the following property: There exists an ordered field \(F\) such that \(x^n+ y^n = z^n\) has solutions in \(F\) with \(xyz \ne 0\). … Continue reading →

Posted in Mathematics | Tagged , , | 6 Comments

Ramanujan Machine Redux

Posted on February 11, 2021 by Persiflage

I had no intention to discuss the Ramanujan Machine again, but over the past few days there has been a flurry of (attempted) trollish comments on that post, so after taking a brief look at the latest version, I thought … Continue reading →

Posted in Mathematics, Rant | Tagged , , | 8 Comments

Hire my students!

Posted on November 18, 2020 by Persiflage

I have three students graduating this year: Shiva Chidambaram, Eric Stubley, and Noah Taylor. In light of the last post, I should give them a boost by reminding you of their (numerous) results which have been discussed on this blog. … Continue reading →

Posted in Mathematics, Work of my students | Tagged , | Leave a comment

The upcoming jobs bloodbath

Posted on November 12, 2020 by Persiflage

Universities are losing lots of money this year. Even those schools with a sizeable endowment are very restricted in how those funds can be used, and the result is that many places will have hiring freezes. This is surely going … Continue reading →

Posted in Politics | Tagged , , | 9 Comments