Category Archives: Mathematics

Giving a good mathematics talk

Posted on November 2, 2024 by Persiflage

Last week, Tadashi Tokieda came to Chicago to give a colloquium. If you have seen him speak, you will not be surprised to learn that it was absolutely delightful talk. I carried the talk around with me in my mind … Continue reading →

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Walter Neumann

Posted on September 30, 2024 by Persiflage

I recently learnt the sad news that Walter Neumann just passed away. Although I don’t think I have seen him in person for over 25 years, Walter was a pretty significant influence in my mathematical life. Here are some of … Continue reading →

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Not quite what I meant

Posted on August 15, 2024 by Persiflage

Weibo Fu wrote an interesting paper on upper bounds for spaces of Bianchi modular forms, pushing previous results of Simon Marshall and Yongquan Hu to get more or less optimal results in the weight aspect. More generally, for any number … Continue reading →

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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 →

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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 →

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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 →

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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 →

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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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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 →

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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 →

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