Tag Archives: Grothendieck

30 years of modularity: number theory since the proof of Fermat

Posted on July 8, 2022 by Persiflage

It’s probably fair to say that the target audience for this blog is close to orthogonal to the target audience for my talk, but just in case anyone wants to watch it in HD (and with the audio synced to … Continue reading →

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The paramodular conjecture is false for trivial reasons

Posted on January 15, 2018 by Persiflage

(This is part of a series of occasional posts discussing results and observations in my joint paper with Boxer, Gee, and Pilloni mentioned here.) Brumer and Kramer made a conjecture positing a bijection between isogeny classes of abelian surfaces \(A/\mathbf{Q}\) … Continue reading →

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The ABC conjecture has (still) not been proved

Posted on December 17, 2017 by Persiflage

The ABC conjecture has (still) not been proved. Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of … Continue reading →

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The decline and fall of Publications Mathématiques de l’lHÉS

Posted on August 15, 2014 by Persiflage

I want to discuss the decline of a once great journal. How did IHES go from this: and this: to this: It is a sad state of affairs. To be clear, I am talking about the typesetting here. The old … Continue reading →

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Effective Motives

Posted on July 3, 2013 by Persiflage

This is a brief follow up concerning a question asked by Felipe. Suppose we assume the standard conjectures. Let \(M\) be a pure motive, and consider the following problems: Problem A: (“effectivity”) Suppose that \(M\) has non-negative Hodge-Tate weights. Then … Continue reading →

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The Two Cultures of Mathematics: A Rebuttal

Posted on December 12, 2012 by Persiflage

Gowers writes thoughtfully about combinatorics here, in an essay which references Snow’s famous lectures (or famous amongst mathematicians – I’ve never met anyone else who has ever heard of them). The trouble, however, starts (as it often does) with the … Continue reading →

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