Author Archives: Persiflage

Persiflage, 2012-2024

Posted on July 23, 2024 by Persiflage

No, not a eulogy! I’ve been a bit concerned for a while about how stable wordpress is as a website — various plugins are always updating on their own, and I have sometimes noticed that old blog posts do not … Continue reading →

Posted in Uncategorized, Waffle | Tagged , , , | 2 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

A talk on my new work with Vesselin Dimitrov and Yunqing Tang on irrationality

Posted on June 16, 2024 by Persiflage

Here is a video of my talk from the recent 70th birthday conference of Peter Sarnak. During a talk one always forgets to say certain things, so I realized that my blog could be a good place to give some … Continue reading →

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

Zeilberger + ChatGPT

Posted on June 1, 2024 by Persiflage

Since I don’t have maple, I can’t play with the following code: https://sites.math.rutgers.edu/~zeilberg/tokhniot/MultiAlmkvistZeilberger.txt But is ChatGPT now good enough to re-write this in either pari/gp or magma (or Mathematica). I’m not sure how realistic this might be (without some serious … Continue reading →

Posted in Mathematics | Tagged , , | 2 Comments

Unramified Fontaine-Mazur for representations coming from abelian varieties

Posted on May 9, 2024 by Persiflage

Mark Kisin gave a talk at the number theory seminar last week where the following problem arose: Let \(W\) be the Galois representation associated to the Tate module of an abelian variety \(A\) over a number field, and suppose that … Continue reading →

Posted in Mathematics | Tagged , | 4 Comments

Midlife crisis

Posted on February 12, 2024 by Persiflage

Plein Air is certainly the best cafe in Hyde Park. (Arguably Build Coffee is fine as well, but they are only open about 5 hours a week.) But it is also true to say that Plein Air is (at best) … Continue reading →

Posted in Coffee | 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

Magma Instability

Posted on October 13, 2023 by Persiflage

I had occasion to return to some magma scripts I wrote in 2012. I the script used a number of pre-computed auxiliary files with computations, and was a little complicated, but didn’t use anything particularly complicated. So I was really … Continue reading →

Posted in Mathematics | Tagged , | 3 Comments

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

Clozel 70, Part I

Posted on September 24, 2023 by Persiflage

I recently returned home from a trip to Paris for Clozel’s 70th birthday conference. Naturally I stayed in an airbnb downtown, and the RER B gods smiled on me with a hassle free commute for the entire week. Tekés was … Continue reading →

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