Author Archives: Persiflage

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 →

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

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 →

Posted in Mathematics, Music, Students | Tagged , , , , , , , , , , , , , , | 3 Comments

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

En Passant VI

Posted on October 29, 2019 by Persiflage

I just learnt (from a comment on this blog) that Pierre Colmez hosts a wonderful page on Fontaine and Wintenberger here. I particularly recommend reading both the personal recollections of their friends and collaborators (sample quote from Mark: These \(p\)-adic … Continue reading →

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Appropriate Citations

Posted on October 27, 2019 by Persiflage

Once I wrote a paper (two, in fact) on even Galois representations. The second paper in particular proved what I thought was a fairly definitive result ruling out the existence of a wide class of even de Rham representations with … Continue reading →

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