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Meta
Tag Archives: Langlands
Graduation Day
This last summer, I undertook my last official activity as a faculty member at Northwestern University, namely, graduation day! (I had a 0% courtesy appointment for two years until my last Northwestern students graduated.) Here I am with four of … Continue reading
New Results In Modularity, Part I
I usually refrain from talking directly about my papers, and this reticence stems from wishing to avoid any appearance of tooting my own horn. On the other hand, nobody else seems to be talking about them either. Moreover, I have … Continue reading
Posted in Mathematics
Tagged Ana Caraiani, Andrew Wiles, Bao Le Hung, Blasius, David Geraghty, David Helm, Deligne, Don Blasius, Functoriality, Gowers, Jack Thorne, James Newton, Langlands, Laurent Clozel, Michael Harris, Modularity, Nuno Freitas, Patrick Allen, Peter Scholze, Port, Ramanujan, Reciprocity, RLT, Samir Siksek, Serre, The Triangle, Toby Gee
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LMFDB!?
The LMFDB has gone live! I previously expressed on this blog a somewhat muted opinion about certain aspects of the website’s functionality, and it seems that my complaints have mainly been addressed in the latest version. On the other hand, … Continue reading
Posted in Mathematics, Rant
Tagged Cremona, Cris Poor, David Yuen, John Voight, Langlands
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Review of Buzzard-Gee
This is a review of the paper “Slopes of Modular Forms” submitted for publication in a Simons symposium proceedings volume. tl;dr: This paper is a nice survey article on questions concerning the slopes of modular forms. Buzzard has given a … Continue reading
Derived Langlands
Although it has been in the air for some time, it seems as though ideas from derived algebraic geometry have begun to inform developments in the Langlands program. (A necessary qualifier: I am talking about reciprocity in the classical arithmetic … Continue reading
The Artin conjecture is rubbish
Let \(\rho: G_{\mathbf{Q}} \rightarrow \mathrm{GL}_N(\mathbf{C})\) be a continuous irreducible representation. Artin conjectured that the L-function \(L(\rho,s)\) is analytically continues to an entire function on \(\mathbf{C}\) (except for the trivial representation where the is a simple pole at one) and satisfies … Continue reading
Posted in Mathematics
Tagged Andrew Booker, Artin, Cebotarev Density Theorem, Class Number Problem, Dick Gross, Goldfeld, GRH, Jo Dwyer, Langlands, Rubbish, Springer, Stark, Zagier
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Scholze on Torsion, Part IV
This is a continuation of Part I, Part II, and Part III. I was planning to start talking about Chapter IV, instead, this will be a very soft introduction to a few lines on page 72. At this point, we … Continue reading
Scholze on Torsion, Part III
This is a continuation of Part I and Part II. Before I continue along to section V.3, I want to discuss an approach to the problem of constructing Galois representations from the pre-Scholze days. Let’s continue with the same notation … Continue reading
Posted in Mathematics
Tagged Galois Representations, Langlands, Peter Scholze, torsion, Vaporware
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