Author Archives: Persiflage

Jacquet-Langlands and a new R=T conjecture

Posted on January 8, 2019 by Persiflage

It is somewhat mysterious how one should formulate the Jacquet-Langlands correspondence integrally, particularly in the presence of torsion classes. Even the classical case has many subtleties including for example some results in this paper of Ribet. In the case of … Continue reading →

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And then there were 8:

Posted on January 6, 2019 by Persiflage

News from Minnesota on the 8-author paper has arrived! http://math.uchicago.edu/~fcale/blog/8author.mp4

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Organization

Posted on December 31, 2018 by Persiflage

This is the current state of my inbox: That either makes me very efficient and up to date, or simply very unpopular (or both!) I’m ready for the new year!

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New Results In Modularity, Christmas Update

Posted on December 25, 2018 by Persiflage

It’s a Christmas miracle! Keen watchers of this blog will be happy to learn that the 10 author paper discussed here and here is now available. (And just in case you also missed it, you can also find the other … Continue reading →

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Guess That Tune!

Posted on December 18, 2018 by Persiflage

I have recent upgraded my wheels from “classic” (20th century corolla, slightly used) to “contemporary” (21st century corolla, also slightly used). Possibly the last straw was when I found the article Toyota Recalls 1993 Camry Due To Fact That Owners … Continue reading →

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A strange continuity

Posted on November 25, 2018 by Persiflage

Returning to matters OPAQUE, here is the following problem which may well now be approachable by known methods. Let me phrase the conjecture in the case when the prime p = 2 and the level N = 1. As we … Continue reading →

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Hausdorff Trimester: May 4-August 21, 2020

Posted on November 18, 2018 by Persiflage

This post is to let everyone know that there will be a trimester at the Hausdorff institute in 2020 organized by Ana Caraiani, Laurent Fargues, Peter Scholze, and myself on “The Arithmetic of the Langlands Program“. The dates for both … Continue reading →

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Irregular Lifts, Part II

Posted on October 28, 2018 by Persiflage

This is the global counterpart to the last post. I was going to write this post in a more general setting, but the annoyances of general reductive groups got the better of me. Suppose we fix the following: A number … Continue reading →

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Irregular Lifts, Part I

Posted on October 19, 2018 by Persiflage

This post motivated in part by the recent preprint of Fakhruddin, Khare, and Patrikis, and also by Matt’s number theory seminar at Chicago this week. (If you are interested in knowing what the calendar is for the Chicago number theory … Continue reading →

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More or less OPAQUE

Posted on October 16, 2018 by Persiflage

I recently talked with Lynnelle Ye (a soon to be graduating student of Mark Kisin) for a few hours about her thesis and related mathematics. In her thesis, she generalizes (in part) the work Liu-Wan-Xiao on the boundary (halo) of … Continue reading →

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