Author Archives: Persiflage

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 →

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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 →

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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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A homework exercise for Oaxaca

Posted on October 12, 2019 by Persiflage

Here’s a homework problem for those coming to Oaxaca who have a facility for working with Breuil-Kisin modules and finite flat group schemes. Let \(\mathbf{F}\) be a finite field of characteristic \(p\), and consider a Galois representation: \(\rho: G_{\mathbf{Q}_p} \rightarrow … Continue reading →

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Read my NSF proposal

Posted on October 9, 2019 by Persiflage

Since this is NSF season, I took the opportunity to go back and look at some of my old proposals. I am definitely too shy to put my *most recent* proposal online, but I thought it might be interesting to … Continue reading →

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I asked… and you responded!

Posted on September 30, 2019 by Persiflage

I often ask mathematical questions on this blog that I don’t know how to answer. Sometimes my smart readers are able to answer the questions I ask. Surely they deserve some recognition for this? Here are two such occasions which … Continue reading →

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