Tag Archives: Toby Gee

The Arthurian Legend

Posted on October 18, 2024 by Persiflage

Some time back, Kevin Buzzard (friend of the blog!) gave a series of talks in which he criticized certain aspects of the mathematical culture when it came to accepting proof. In addition to obvious targets like the classification of finite … Continue reading →

Posted in Uncategorized | Tagged , , , , , , , , , , , , , , , , , | 6 Comments

SL_n versus GL_n

Posted on July 18, 2024 by Persiflage

I recently wrote a paper (with Toby Gee and George Boxer, see also here) on constructing regular algebraic automorphic representations \(\pi\) of (cohomological) weight zero and level one, and therefore also cuspidal cohomology classes in the cohomology of \(\mathrm{GL}_n(\mathbf{Z})\) for … Continue reading →

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

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 →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Clozel 70, Part II

Posted on September 30, 2023 by Persiflage

Many years ago, Khare asked me (as I think he asked many others at the time) whether I believed their existed an irreducible motive \(M\) over \(\mathbf{Z}\) (so good reduction everywhere) with Hodge-Tate weights \([0,1,2,\ldots,n-1]\) for any \(n > 1\). … Continue reading →

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

Boxes for Boxer update

Posted on February 28, 2023 by Persiflage

As noted in this post, exactly 42 reprints of [BCGP] were recovered in January of 2022 from boxes left out in the snow outside Eckhart Hall addressed to George Boxer. As mentioned there, the packaging (5 boxes of 8 plus … Continue reading →

Posted in Rant | Tagged , , , , , | 1 Comment

Potential Modularity of K3 surfaces

Posted on November 15, 2022 by Persiflage

This post is to report on results of my student Chao Gu who is graduating this (academic) year. If \(A/F\) is an abelian surface, then one can associate to \(A\) a K3 surface \(X\) (the Kummer surface) by blowing up … Continue reading →

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

30 years of modularity: number theory since the proof of Fermat

Posted on July 8, 2022 by Persiflage

It’s probably fair to say that the target audience for this blog is close to orthogonal to the target audience for my talk, but just in case anyone wants to watch it in HD (and with the audio synced to … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Boxes for Boxer

Posted on January 4, 2022 by Persiflage

My brother texted me on Monday saying that there were seven (or so) boxes pilled up (outside!) in front of the mathematics department and all addressed to George Boxer. My first thought was that this was a transatlantic move gone … Continue reading →

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

Potential Automorphy for GL(n)

Posted on April 29, 2021 by Persiflage

Fresh on the arXiv, a nice new paper by Lie Qian proving potential automorphy results for ordinary Galois representations \(\rho: G_F \rightarrow \mathrm{GL}_n(\mathbf{Q}_p)\) of regular weight \([0,1,\ldots,n-1]\) for arbitrary CM fields \(F\). The key step in light of the 10-author … Continue reading →

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

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