Author Archives: Persiflage

What would a good ICM talk look like?

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

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

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

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

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

59,281

The target audience of this blog (especially the mathematics) is usually professional mathematicians in the Langlands program. I do sometimes, however, have posts suitable for a broader mathematical audience. Very rarely though do I have anything (possibly) interesting to say … Continue reading

Posted in Mathematics | Tagged , , , , , , , , | 14 Comments

Divisors near sqrt(n)

Analytic Number Theory Alert! An even more idle question than normal (that’s because it comes from twitter). Alex Kontorovich noted with pleasure the following pictorial representation of the integers from a Veritasium youtube video, where prime numbers are represented by … Continue reading

Posted in Mathematics | Tagged , , , | 5 Comments

Potential Automorphy for GL(n)

Fresh on the arXiv, a nice new paper by Lie Qian proving potential automorphy results for ordinary Galois representations \(\rho: G_F \rightarrow \mathrm{GL}_n(\mathbf{Q}_p)\) of regular weight \([0,1,\ldots,n-1]\) for arbitrary CM fields \(F\). The key step in light of the 10-author … Continue reading

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

Don’t cite my paper!

The process of publishing a paper is an extremely long one, and it is not atypical to take several years from the first submission to the paper finally being accepted. The one part of the process that happens extremely quickly, … Continue reading

Posted in Rant | Tagged , , | 18 Comments

The Arbeitsgemeinschaft has returned!

An update on this post; the Arbeitsgemeinschaft on derived Galois deformation rings and the cohomology of arithmetic groups will now be taking place the week of April 5th. Here is some practical information if you are curious. Is there somewhere … Continue reading

Posted in Mathematics | Tagged , , | 2 Comments