Category Archives: Mathematics

Central Extensions and Weight One Forms

Posted on May 23, 2016 by Persiflage

As mentioned in the comments to the last post, Kevin Buzzard and Alan Lauder have made an extensive computation of weight one modular forms in characteristic zero (see also here). Thinking about what that data might contain, I wondered about … Continue reading →

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

LMFDB!?

Posted on May 12, 2016 by Persiflage

The LMFDB has gone live! I previously expressed on this blog a somewhat muted opinion about certain aspects of the website’s functionality, and it seems that my complaints have mainly been addressed in the latest version. On the other hand, … Continue reading →

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

Report From Berkeley

Posted on April 22, 2016 by Persiflage

My recent trip to Berkeley did not result in a chance to test whether the Cheeseboard pizza maintained its ranking, but did give me the opportunity to attend the latest Bay Area Number Theory and Algebraic Geometry day, on a … Continue reading →

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

Tensor Products

Posted on March 28, 2016 by Persiflage

Let \(W\) be an irreducible representation of a finite group \(G.\) Say that \(W\) is tensor indecomposable if any isomorphism \(W = U \otimes V\) implies that either \(U\) or \(V\) is a character. In conversations with Matt and Toby … Continue reading →

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

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 →

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

Counting solutions to a_p = λ

Posted on May 15, 2015 by Persiflage

We know that the eigenvalue of \(T_2\) on \(\Delta\) is \(24.\) Are there any other level one cusp forms with the same Hecke eigenvalue? Maeda’s conjecture in its strongest form certainly implies that there does not. But what can one … Continue reading →

Posted in Mathematics | Tagged , , , , | 4 Comments

144169

Posted on May 12, 2015 by Persiflage

The space of classical modular cuspforms of level one and weight 24 has dimension two — the smallest weight for which the dimension is not zero or one. What can we say about the Hecke algebra acting on this space … Continue reading →

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

Chenevier on the Eigencurve

Posted on April 24, 2015 by Persiflage

Today I wanted to mention a theorem of Chenever about components of the Eigencurve. Let \(\mathcal{W}\) denote weight space (which is basically a union of discs), and let \(\pi: \mathcal{E} \rightarrow \mathcal{W}\) be the Coleman-Mazur eigencurve together with its natural … Continue reading →

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

The seven types of graduate student applicant

Posted on March 29, 2015 by Persiflage

Yes, it’s that time of year again. Hide and Seek: Contacts you every day about the status of their application, then goes on radio silence the moment they receive an offer, never to be heard of again. The No Chancer: … Continue reading →

Posted in Mathematics, Rant | Tagged , , | 11 Comments

Review of Buzzard-Gee

Posted on March 3, 2015 by Persiflage

This is a review of the paper “Slopes of Modular Forms” submitted for publication in a Simons symposium proceedings volume. tl;dr: This paper is a nice survey article on questions concerning the slopes of modular forms. Buzzard has given a … Continue reading →

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