Category Archives: Students

The horizontal Breuil-Mezard conjecture

Posted on October 19, 2023 by Persiflage

Postdoc hiring season will be upon us soon! I have two excellent graduate students who will be applying for academic jobs soon, Chengyang Bao and Andreea Iorga. I have mentioned Chengyang’s first project before here and an introduction to the … Continue reading →

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Locally induced representations

Posted on June 16, 2022 by Persiflage

Today is a post about work of my student Chengyang Bao. Recall that Lehmer’s conjecture asks whether \(\tau(p) \ne 0\) for all primes \(p\), where \(\Delta = q \prod_{n=1}^{\infty} (1 – q^n)^{24} = \sum \tau(n) q^n\) is Ramanujan’s modular form. … Continue reading →

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Murphy’s Law for Galois Deformation Rings

Posted on April 23, 2022 by Persiflage

Today’s post is about work of my student Andreea Iorga! A theorem of Ozaki from 2011, perhaps not as widely known as expected, says the following: Theorem: Let \(p\) be prime, and let \(G\) be a finite \(p\)-group. Then there … Continue reading →

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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 →

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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 →

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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 →

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Chidambaram on genus two curves, I

Posted on April 15, 2020 by Persiflage

Before we start, just to alert you to a minor blogpage design change: all the posts (including this one) which talk about my students work can be accessed in one place by clicking the “work of my students” tab just … Continue reading →

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The last seven words of Kedlaya-Medvedovsky

Posted on January 14, 2020 by Persiflage

New paper by my student Noah Taylor! It addresses some conjectures raised by Kedlaya and Medvedovsky in this paper. Let \(\mathbf{T}\) denote the Hecke algebra acting on modular forms of weight two and prime level \(N\) generated by Hecke operators … Continue reading →

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Update on Sato-Tate for abelian surfaces

Posted on July 19, 2018 by Persiflage

Various people have asked me for an update on the status of the Sato-Tate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading →

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Schaefer and Stubley on Class Groups

Posted on October 28, 2017 by Persiflage

I talked previously about work of Wake and Wang-Erickson on deformations of Eisenstein residual representations. In that post, I also mentioned a paper of Emmanuel Lecouturier who has also proved some very interesting theorems. Today, I wanted to talk about … Continue reading →

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