Tag Archives: Jordan Ellenberg

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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Mazur 80

Posted on June 10, 2018 by Persiflage

Last week I was in Cambridge for Barry’s 80th birthday conference. If you are wondering why it took so long for Barry to get a birthday conference, that’s probably because you didn’t know that there was *also* a 60th birthday … Continue reading →

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The class number 100 problem

Posted on January 19, 2017 by Persiflage

Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading →

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Hilbert Modular Forms of Partial Weight One, Part III

Posted on October 17, 2015 by Persiflage

My student Richard Moy is graduating! Richard’s work has already appeared on this blog before, where we discussed his joint work with Joel Specter showing that there existed non-CM Hilbert modular forms of partial weight one. Today I want to … Continue reading →

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How not to be wrong

Posted on May 7, 2015 by Persiflage

I recently finished listening to Jordan’s book “how not to be wrong,” and thought that I would record some of the notes I made. Unlike other reviews, Persiflage will cut through to the key aspects of the book which perhaps … Continue reading →

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Math and Genius

Posted on June 6, 2014 by Persiflage

Jordan Ellenberg makes a compelling case, as usual, on the pernicious cultural notion of “genius.” Jordan’s article also brought to mind a thought provoking piece on genius by Moon Duchin here (full disclosure: the link on Duchin’s website has the … Continue reading →

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The Thick Diagonal

Posted on March 14, 2014 by Persiflage

Suppose that \(F\) is an imaginary quadratic field. Suppose that \(\pi\) is a cuspidal automorphic form for \(\mathrm{GL}(2)/F\) of cohomological type, and let us suppose that it contributes to the cohomology group \(H^1(\Gamma,\mathbf{C})\) for some congruence subgroup \(\Gamma\) of \(\mathrm{GL}_2(\mathcal{O}_F)\). … Continue reading →

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The problem with baseball

Posted on October 27, 2013 by Persiflage

Jordan Ellenberg, in a lovely slate article, explains perfectly what I don’t like about baseball. I think the fundamentals of baseball as a sport are sound. I like the pace of the game, the variation, the statistics, the quirkiness, the … Continue reading →

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Virtual Congruence Betti Numbers

Posted on September 27, 2013 by Persiflage

Suppose that \(G\) is a real semisimple group and that \(X = \Gamma \backslash G/K\) is a compact arithmetic locally symmetric space. Let us call a cohomology class tautological if it is invariant under the group \(G\). For example, if … Continue reading →

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