Tag Archives: Richard Moy

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

Families of Hilbert Modular Forms of Partial Weight One.

Today I would like to talk about a beautiful new theorem of my student Eric Stubley (see also here). The first version of Eric’s result assumed (unknown) cases of the general Ramanujan conjecture for Hilbert modular forms, and relied on … Continue reading

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , , , , | 2 Comments

More on Lehmer’s Conjecture

Lehmer said it was a “natural question” whether there existed an integer such that \(\tau(n)=0\) or not. I’ve wondered a little bit recently about how reasonable this is. (See this post.) The historical context is presumably related to the fact … Continue reading

Posted in Uncategorized | Tagged , , , , , , , , , | 11 Comments

Graduation Day

This last summer, I undertook my last official activity as a faculty member at Northwestern University, namely, graduation day! (I had a 0% courtesy appointment for two years until my last Northwestern students graduated.) Here I am with four of … Continue reading

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

Hilbert Modular Forms of Partial Weight One, Part III

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

Posted in Mathematics, Students | Tagged , , , , , , , , , , | Leave a comment

En Passant IV

My students Richard Moy and Joel Specter have uploaded their paper on partial weight one Hilbert modular forms, previously discussed here, to the ArXiv. Germany now leads the world in both soccer and perfectoid spaces. This is a recipe for … Continue reading

Posted in Waffle | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Hilbert Modular Forms of Partial Weight One, Part II

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

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