Author Archives: Persiflage

Deciphering Quanta

Posted on March 23, 2023 by Persiflage

Sometimes it is claimed that Quanta articles are so watered down of mathematical content that they become meaningless. That presents a challenge: do I understand the quanta article on my own work? Here goes: New Proof Distinguishes Mysterious and Powerful … Continue reading →

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Boxes for Boxer update

Posted on February 28, 2023 by Persiflage

As noted in this post, exactly 42 reprints of [BCGP] were recovered in January of 2022 from boxes left out in the snow outside Eckhart Hall addressed to George Boxer. As mentioned there, the packaging (5 boxes of 8 plus … Continue reading →

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What the slopes are

Posted on February 25, 2023 by Persiflage

Let \(f\) be a classical modular eigenform of weight \(k\), for example, \(f = \Delta\). The Ramanujan conjecture states that the Hecke eigenvalues \(a_p\) satisfy the bound \(|a_p| \le 2 p^{(k-1)/2}.\) A slightly fancier but cleaner way of saying this … Continue reading →

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Check the arXiV regularly!

Posted on February 18, 2023 by Persiflage

In a previous post, I discussed a new result of Smith which addressed the following question: given a measure \(\mu\) on \(\mathbf{R}\) supported on some finite union of intervals \(\Sigma\), under what conditions do there exist polynomials of arbitrarily large … Continue reading →

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Report from Australia, Part I, Coffee

Posted on February 15, 2023 by Persiflage

My travel often involves making some effort to find good local coffee. From Palo Alto to Portland, a little effort finds quality cafes with reliable espresso drinks. How does the rest of the world then stack up with Australia, the … Continue reading →

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Potential Modularity of K3 surfaces

Posted on November 15, 2022 by Persiflage

This post is to report on results of my student Chao Gu who is graduating this (academic) year. If \(A/F\) is an abelian surface, then one can associate to \(A\) a K3 surface \(X\) (the Kummer surface) by blowing up … Continue reading →

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Peak Hyde Park

Posted on November 12, 2022 by Persiflage

Me dressed as a crocodile chasing the Groke while being chased by Drinfeld down Harper Ave on Halloween (all in front of a 16 foot inflatable pumpkin). Sadly, Drinfeld was not dressed as a Shtuka.

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The future is now; recap from Cetraro

Posted on July 31, 2022 by Persiflage

I’ve just returned from the second Journal of Number Theory biennial conference in Italy. It’s always nice to get a chance to see slices of number theory one wouldn’t otherwise see at the conferences I usually go to (although this … Continue reading →

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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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Locally induced representations

Posted on June 16, 2022 by Persiflage

Today is a post about work of my student Chengyang Bao. Recall that Lehmer’s conjecture asks whether \(\tau(p) \ne 0\) for all primes \(p\), where \(\Delta = q \prod_{n=1}^{\infty} (1 – q^n)^{24} = \sum \tau(n) q^n\) is Ramanujan’s modular form. … Continue reading →

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