Author Archives: Persiflage

Joël Bellaïche

Posted on June 14, 2022 by Persiflage

Very sad to hear that Joël Bellaïche has just died. He got his PhD at the same time as me, and I first got to know him during the Durham conference in 2004 and later at the eigenvarieties semester at … Continue reading →

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

Murphy’s Law for Galois Deformation Rings

Posted on April 23, 2022 by Persiflage

Today’s post is about work of my student Andreea Iorga! A theorem of Ozaki from 2011, perhaps not as widely known as expected, says the following: Theorem: Let \(p\) be prime, and let \(G\) be a finite \(p\)-group. Then there … Continue reading →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , | 11 Comments

What would Deuring do?

Posted on April 13, 2022 by Persiflage

This is an incredibly lazy post, but why not! Matt is running a seminar this quarter on the Weil conjectures. It came up that one possible way to prove the Weil conjectures for elliptic curves over finite fields is to … Continue reading →

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

A random curve over Q

Posted on April 2, 2022 by Persiflage

Let \(X/\mathbf{Q}\) be a smooth projective curve. I would like to be able to say that the motive \(M\) associated to \(X\) “generally” determines \(X\). That is, I would like to say it in a talk without feeling like I’m … Continue reading →

Posted in Mathematics | Tagged , , | 16 Comments

ArXiv x 3

Posted on March 4, 2022 by Persiflage

Three recent arXiv preprints this week caught my interest and seemed worth mentioning here. The first is a paper by Oscar Randal-Williams, which considers (among other things) the cohomology of congruence subgroups of \(\mathrm{SL}_N(\mathbf{Z})\) in the stable range. This is … Continue reading →

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What would a good ICM talk look like?

Posted on February 27, 2022 by Persiflage

Now that the ICM has (unsurprisingly) become a virtual event, it might be worthwhile thinking a little bit about what would constitute a good talk in this new setting. There’s a certain electricity to talks given in person, and I … Continue reading →

Posted in Mathematics, Politics | Tagged , , , , | 3 Comments

Boxes for Boxer

Posted on January 4, 2022 by Persiflage

My brother texted me on Monday saying that there were seven (or so) boxes pilled up (outside!) in front of the mathematics department and all addressed to George Boxer. My first thought was that this was a transatlantic move gone … Continue reading →

Posted in Mathematics | Tagged , , , , | 6 Comments

Simons Annual Meeting

Posted on December 23, 2021 by Persiflage

The last time I traveled for math was when I gave the Coble lectures at UIUC pre-pandemic (at least pre-pandemic as far as the US goes). A few months ago it seemed like one could begin to start traveling again, … Continue reading →

Posted in Mathematics, Travel | 3 Comments

Schur-Siegel-Smyth-Serre-Smith

Posted on November 25, 2021 by Persiflage

If \(\alpha\) is an algebraic number, the normlized trace of \(\alpha\) is defined to be \( \displaystyle{T(\alpha):=\frac{\mathrm{Tr}(\alpha)}{[\mathbf{Q}(\alpha):\mathbf{Q}].}}\) If \(\alpha\) is an algebraic integer that is totally positive, then the normalized trace is at least one. This follows from the AM-GM … Continue reading →

Posted in Mathematics | Tagged , , , , , | 5 Comments

Polymath Proposal: 4-folds of Mumford’s type

Posted on August 24, 2021 by Persiflage

Let \(A/K\) be an abelian variety of dimension \(g\) over a number field. If \(g \not\equiv 0 \bmod 4\) and \(\mathrm{End}(A/\mathbf{C}) = \mathbf{Z}\), then Serre proved that the Galois representations associated to \(A\) have open image in \(\mathrm{GSp}_{2g}(\mathbf{Z}_p)\). The result … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , | 2 Comments