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Meta
Tag Archives: Serre
Walter Neumann
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
SL_n versus GL_n
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 AI, ChatGPT, Gaëtan Chenevier, George Boxer, Go, Grunwald-Wang Theorem, Hilbert modular forms, Jack Thorne, James Newton, Jean-Pierre Labesse, Joachim Schwermer, John Tate, Jürgen Rohlfs, Karen Vogtmann, la langue française, Laurent Clozel, Nasit Darshan, Pierre Colmez, Raghuram, Serre, Serre-Tate Correspondence, Stefan Patrikis, Tate, Toby Gee
1 Comment
Schur-Siegel-Smyth-Serre-Smith
If \(\alpha\) is an algebraic number, the normlized trace of \(\alpha\) is defined to be \( \displaystyle{T(\alpha):=\frac{\mathrm{Tr}(\alpha)}{[\mathbf{Q}(\alpha):\mathbf{Q}].}}\) If \(\alpha\) is an algebraic integer that is totally positive, then the normalized trace is at least one. This follows from the AM-GM … Continue reading
Posted in Mathematics
Tagged Alex Smith, Chris Smyth, Cyclotomic Fields, Schur, Serre, Siegel Modular Forms
5 Comments
Update on Sato-Tate for abelian surfaces
Various people have asked me for an update on the status of the Sato-Tate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading
Posted in Mathematics, Students
Tagged Ana Caraiani, Andrew Sutherland, Andrew Wiles, Bao Le Hung, Christian Johansson, David Helm, Francesc Fité, Freydoon Shahidi, George Boxer, Henry Kim, Jack Thorne, James Newton, Kiran Kedlaya, Laurent Clozel, Michael Harris, Nick Katz, Noah Taylor, Patrick Allen, Peter Scholze, Potential Modularity, Richard Taylor, Sato-Tate, Serre, Toby Gee, Victor Rotger, Vincent Pilloni
3 Comments
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
13 Comments
Correspondance Serre-Tate, Part I
Reading the correspondence between Serre and Tate has been as delightful as one could expect. What is very nice to see — although perhaps not so surprising — is the utter delight that both Serre and Tate find in discussing … Continue reading
Posted in Mathematics
Tagged 118982593, 144169, 3457, 691, 97, Deuring, minus part, Mumford, Odlyzko, plus part, Rene Schoof, Serre, Serre-Tate Correspondence, Tate, Tate Conjecture
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Indulgences
Today is Persiflage’s birthday, but let us not also forget to wish many happy returns to friends of the blog Ana and Vytas, who share the same birthday! Here is how I plan to celebrate: I will spare you with the … Continue reading
Posted in Food
Tagged Ana Caraiani, Bach, Bao Le Hung, Champagne, Fog, Foie Gras, Fruit Cake, King's College Cambridge, Lake Michigan, Musical Offering, Sauternes, Schubert, Serre, Serre-Tate Correspondence, Smoked Eel, Tallis, Tate, Tea, Tofu, Vytas Paskunas
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Serre 1: Calegari 0
I just spent a week or so trying to determine whether Serre’s conjecture about the congruence subgroup property was false for a very specific class of S-arithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading
Posted in Mathematics
Tagged Contradictions, CSP, Fred Diamond, Fred Diamond's Beard, George Boxer, Ihara's Lemma, John Voight, Keerthi, Ken Ribet, Mathematica, Matthew Emerton, RLT, Serre
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Ventotene, Part II
I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading
Posted in Uncategorized
Tagged Akshay Venkatesh, Borel, completed cohomology, Nicolas Bergeron, Peter Scholze, Serre, torsion
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