Category Archives: Students

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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Abelian Spiders

Posted on January 11, 2015 by Persiflage

This is a blog post about the thesis of my student Zoey Guo, who is graduating this year. (For a blog post on the thesis of my other student graduating this year, see this.) Let \(\Phi\) be a finite graph. … Continue reading →

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Thurston, Selberg, and Random Polynomials, Part I.

Posted on May 21, 2014 by Persiflage

Apart from everything else, you could always count on Bill Thurston to ask interesting questions. This is the first of a small number of posts which were motivated in part by figure two from this paper, and this accompanying MO … 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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Hilbert Modular Forms of Partial Weight One, Part II

Posted on December 8, 2012 by Persiflage

Anyone who spends any time thinking about Hilbert modular forms of partial weight one — see part I — should, at some point, wonder whether there actually exist any examples, besides the “trivial” examples arising as inductions of Grossencharacters. Fred … Continue reading →

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Hilbert Modular Forms of Partial Weight One, Part I

Posted on October 13, 2012 by Persiflage

Let \(\pi\) be an algebraic Hilbert modular cuspform for some totally real field \(F^{+}\). Then, associated to \(\pi\), one has a compatible family of Galois representations: \(r_{\lambda}(\pi): G_{F^{+}} \rightarrow \mathrm{GL}_2(\mathcal{O}_{\lambda})\) which are unramified outside finitely many primes (this is the … Continue reading →

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