Category Archives: Mathematics

The paramodular conjecture is false for trivial reasons

(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 over … Continue reading

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Hiring Season

Lizard 1: Wait, explain again why we bury our young in the sand and thereby place them into mortal peril? Lizard 2: So they develop character! If it was good enough for me, it’s good enough for them. (Feel free … Continue reading

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Abandonware

For a young mathematician, there is a lot of pressure to publish (or perish). The role of for-profit academic publishing is to publish large amounts of crappy mathematics papers, make a lot of money, but at least in return grant … Continue reading

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The ABC conjecture has (still) not been proved

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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Graduation Day

This last summer, I undertook my last official activity as a faculty member at Northwestern University, namely, graduation day! (I had a 0% courtesy appointment for two years until my last Northwestern students graduated.) Here I am with four of … Continue reading

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Abelian Surfaces are Potentially Modular

Today I wanted (in the spirit of this post) to report on some new work in progress with George Boxer, Toby Gee, and Vincent Pilloni. Recal that, for a smooth projective variety X over a number field F unramified outside … Continue reading

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Schaefer and Stubley on Class Groups

I talked previously about work of Wake and Wang-Erickson on deformations of Eisenstein residual representations. In that post, I also mentioned a paper of Emmanuel Lecouturier who has also proved some very interesting theorems. Today, I wanted to talk about … Continue reading

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