
Recent Posts
Categories
Blogroll
Recent Comments
Archives
 July 2017
 June 2017
 May 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 August 2016
 June 2016
 May 2016
 April 2016
 March 2016
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 Akshay Venkatesh Ana Caraiani andras schiff Andrew Wiles Bach Bao Le Hung Barry Mazur BLGGT Borel Bourgeois Pig Chess Class Number Problem Coffee completed cohomology cricket CSO cyclotomic integers David Geraghty David Zywina Deligne Dick Gross Elsevier Fermat Fred Diamond Fred Diamond's Beard Galois Representations Gauss George Boxer Glenn Gould Gowers Grothendieck Harvard Hilbert modular forms Ian Agol Intelligentsia Inverse Galois Problem Jack Thorne James Newton Jared Weinstein Joel Specter John Voight Jordan Ellenberg Ktheory KaiWen Lan Ken Ribet Kevin Buzzard Langlands Leopoldt Conjecture Mark Kisin Matthew Emerton Michael Harris MO modular forms Modularity MSRI Music Nonsense Ouroboros Perfectoid Spaces Peter Scholze Puzzle Richard Moy RLT Robert Coleman Schoenberg Schubert Serre subfactors Tate Third Wave Coffee Tilting Toby Gee torsion Vytas Paskunas Zagier
Meta
Category Archives: Mathematics
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
5 Comments
Elementary Class Groups Updated
In a previous post, I gave a short argument showing that, for odd primes p and N such that the pclass group of is nontrivial. This post is just to remark that the same argument works under weaker hypotheses, namely: … Continue reading
Posted in Mathematics
2 Comments
Who proved it first?
During Joel Specter’s thesis defense, he started out by remarking that the expansion: is a weight one modular forms of level and moreover, for prime, is equal to the number of roots of modulo minus one. He attributed this result … Continue reading
Posted in Mathematics
Tagged Binary Quadratic Forms, Class Field Theory, Dedekind, Euler, Furtwängler, Gauss, Hecke, Hilbert, History, Joel Specter, Jugendtraum, Kronecker, Minkowski, Tagaki, Weber
Leave a comment
A nonliftable weight one form modulo p^2
I once idly asked RLT (around 2004ish) whether one could use BuzzardTaylor arguments to prove that any representation: which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). Galois representations of this flavour … Continue reading
Complain about MSRI day
I will be heading off later this week to the Academic Sponsors’ Day at MSRI, going as Shmuel’s proxy for uchicago. I’m not sure to what extent (if any) there is for me to make policy suggestions, but any comments … Continue reading
Posted in Mathematics, Politics
Tagged Kevin Buzzard, MSRI, SatoTate, Shmuel, University of Chicago, wag
14 Comments