Author Archives: Persiflage

En Passant IX (I’m a Gnu)

Posted on October 28, 2020 by Persiflage

One feature of having an electric piano is the ability to record the accompaniment to songs which (for reasons of timing or otherwise) are quite hard to play and sing at the same time. A possible downside, however, is that … Continue reading →

Posted in Food, Music, Waffle | Tagged , , , , , , , , , , , , | 1 Comment

The eigencurve is (still) proper

Posted on October 23, 2020 by Persiflage

Although I don’t think about it so much anymore, the eigencurve of Coleman-Mazur was certainly one of my first loves. I can’t quite say I learnt about \(p\)-adic modular forms at my mother’s knee, but I did spend a formative … Continue reading →

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

Chidambaram on Galois representations (not) associated to abelian varieties over Q

Posted on October 13, 2020 by Persiflage

Today’s post is about a new paper by my student Shiva. Suppose that \(A/\mathbf{Q}\) is a principally polarized abelian variety of dimension \(g\) and \(p\) is a prime. The Galois representation on the \(p\)-torsion points \(A[p]\) gives rise to a … Continue reading →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , | 5 Comments

Tips on becoming a computational number theorist

Posted on June 16, 2020 by Persiflage

How would you advise a student who has talents in both the computational and theoretical aspects of algebraic number theory? There is no hard border between computational and theoretical algebraic number theory, but there is a definite computational number theory … Continue reading →

Posted in Uncategorized | Tagged , , , , | 3 Comments

Families of Hilbert Modular Forms of Partial Weight One.

Posted on June 3, 2020 by Persiflage

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

Picard Groups of Moduli Stacks update

Posted on May 27, 2020 by Persiflage

A tiny update on this post. I was chatting with Benson and realized that I may as well ask him directly for a presentation of the mapping class group of a genus two surface. Perhaps unsurprisingly, it can be found … Continue reading →

Posted in Mathematics | Tagged , , , , | 2 Comments

Panel Discussion: Mathematics Research Online

Posted on May 13, 2020 by Persiflage

Odds are high that virtual conferences in mathematics are here to stay. It seems crucial, therefore, to think long and hard about ways to make them work for all participants. We need to have conversations as a community to better … Continue reading →

Posted in Teaching, Travel | Tagged , , | Leave a comment

Picard Groups of Moduli Stacks

Posted on April 30, 2020 by Persiflage

Here are some algebraic geometry musings related to the last post, most of which is hopefully correct. Everything below is secretly over \(\mathbf{Z}[1/6]\) but I think one may as well think about what is happening over \(\mathbf{C}\). Warning: I don’t … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , | 9 Comments

Chidambaram on genus two curves, II

Posted on April 24, 2020 by Persiflage

We now continue a series of posts on the work of my student Shiva Chidambaram. (Click here for part I.) Today I would like to discuss another project with Shiva that was also joint with David Roberts (no, not David … Continue reading →

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

En Passant VIII

Posted on April 23, 2020 by Persiflage

I just found out that Lucien Szpiro recently passed away. I met him only once in late 2018 when I gave the joint NY number theory at CUNY. When I arrived at my hotel (the Gregory) around 10pm, I was … Continue reading →

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