Author Archives: Persiflage

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

Conferences New and Old: Coronavirus Edition

Posted on March 7, 2020 by Persiflage

A number of people have asked me whether the various conferences and workshops I am organizing this summer are still running. I thought I would have a blogpost containing all the current information, which I can update when and if … Continue reading →

Posted in Travel | Tagged , , , , , | 4 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 →

Posted in Mathematics | Tagged , , , , , , , , , , | 4 Comments

Vale instantchess.com

Posted on February 27, 2020 by Persiflage

One of the few time wasting activities I still indulge in is speed chess. (1 minute per player for the entire game is the slowest time control I play online.) There are a number of excellent free online sites available, … Continue reading →

Posted in Chess | Tagged , , | 2 Comments

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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Job Dedication

Posted on January 25, 2020 by Persiflage

Earlier last quarter, I had suffered a fairly poor night from some sort of stomach bug. Unfortunately, I made the ill-advised decision not to cancel my classes and went to work, which involves driving from Evanston to Hyde Park. Things … Continue reading →

Posted in Travel, Waffle | Tagged , , , , | 1 Comment

Inter-universal Teichmüller theory explained

Posted on January 17, 2020 by Persiflage

Normally a message such as the one below would go immediately to the rubbish bin. Fortunately for me, I happened to open it accidentally and thereupon discovered the most cogent explanation to date of IUT. I hereby share with you … Continue reading →

Posted in Rant | Tagged , , , , | 1 Comment

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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