Category Archives: Mathematics

How to reject a paper

Posted on March 31, 2020 by Persiflage

I just had the paper discussed in this post very quickly rejected. Since it was such a short paper, I thought it not too unreasonable to submit it to a strong journal, so I am not terribly disappointed. I can … Continue reading →

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The Hausdorff Trimester has been indefinitely postponed

Posted on March 18, 2020 by Persiflage

I’m not sure if this is 100% official yet, but the Hausdorff Trimester scheduled for this summer has been (unsurprisingly) postponed. This is probably no great surprise to many of you. We have hopes to reschedule it again (perhaps for … Continue reading →

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NSF Proposal, Graduate Fellowship Edition

Posted on March 17, 2020 by Persiflage

Note: I feel as a service to the number theory entertainment complex that I should blog more often in these times, even if it means being less coherent than usual. I might even try to get a few guest posts … Continue reading →

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The Arbeitsgemeinschaft has been indefinitely postponed

Posted on March 11, 2020 by Persiflage

An update on the last post: As you probably already know by now if you are a participant, the Arbeitsgemeinschaft has been indefinitely postponed. The recommendation to do so was made by the organizers as universities rapidly began to recommend … Continue reading →

Posted in Mathematics, Travel | Tagged | 5 Comments

Counting solutions to a_p = λ, Part II

Posted on March 3, 2020 by Persiflage

This is a sequel to this post where the problem of counting eigenforms with \(a_p = \lambda\) and \(\lambda \ne 0\) was considered. Here we report on recent progress in the case \(\lambda = 0\). It is a somewhat notorious … Continue reading →

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Vesselin Dimitrov on Schinzel–Zassenhaus

Posted on February 10, 2020 by Persiflage

Suppose that \(P(x) \in \mathbf{Z}[x]\) is a monic polynomial. A well-known argument of Kronecker proves that if every complex root of \(P(x)\) has absolute value at most 1, then \(P(x)\) is cyclotomic. It trivially follows that, for a non-cyclotomic polynomial, … Continue reading →

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The last seven words of Kedlaya-Medvedovsky

Posted on January 14, 2020 by Persiflage

New paper by my student Noah Taylor! It addresses some conjectures raised by Kedlaya and Medvedovsky in this paper. Let \(\mathbf{T}\) denote the Hecke algebra acting on modular forms of weight two and prime level \(N\) generated by Hecke operators … Continue reading →

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New Results in modularity, Christmas Update II

Posted on December 30, 2019 by Persiflage

Just like last year, once again saint Nick has brought us a bounty of treasures related to Galois representations and automorphic forms in the final week of the year. First there was this paper by Newton and Thorne, proving, among … Continue reading →

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Background for the Hausdorff Summer School

Posted on December 20, 2019 by Persiflage

For those attending the Haussdorf Summer School previously mentioned here, I followed up with the speakers to ask them a little about what background was optimal for getting the most out of their lectures. In particular, I asked them to … Continue reading →

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Mathjobs Application Tips Update

Posted on November 5, 2019 by Persiflage

Previously I wrote about what I considered a “bug” in mathjobs: when letter writers submit their letter, the default time those letters are available is 18 months. But this leads to the following chain of events: An applicant applies for … Continue reading →

Posted in Mathematics | Tagged , | 3 Comments