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Meta
Category Archives: Uncategorized
ArXiv x 3
Three recent arXiv preprints this week caught my interest and seemed worth mentioning here. The first is a paper by Oscar Randal-Williams, which considers (among other things) the cohomology of congruence subgroups of \(\mathrm{SL}_N(\mathbf{Z})\) in the stable range. This is … Continue reading
Posted in Uncategorized
Tagged Andrew Blumberg, Andrew Putman, Benson Farb, Bill Thurston, completed cohomology, congruence subgroups, Dalimil Mazáč, Jordan Ellenberg, Melanie Wood, Michael Mandell, Nigel Boston, Oscar Randal-Williams, Peter Kravchuk, Simon Marshall, Sridip Pal, Thomas Church, Will Hearst, Will Sawin, William Stein
2 Comments
More on Lehmer’s Conjecture
Lehmer said it was a “natural question” whether there existed an integer such that \(\tau(n)=0\) or not. I’ve wondered a little bit recently about how reasonable this is. (See this post.) The historical context is presumably related to the fact … Continue reading
Background for the Hausdorff Summer School
For those attending the Haussdorf Summer School previously mentioned here, I followed up with the speakers to ask them a little about what background was optimal for getting the most out of their lectures. In particular, I asked them to … Continue reading
NSF Application Tips: LaTeX edition
I’ve previously written about applying for an NSF grant here. But for those applying this year, I have a few further technical tips concerning the technical specifications of your LaTeX document. If you are the type of person who uploads … Continue reading
Administrative Note
Ideally nobody will really notice, but this blog has moved from www.galoisrepresentations.wordpress.com to www.galoisrepresentations.com. This blog still runs on the (open source) wordpress system, the only difference is that it is longer hosted by wordpress. The reason for hosting this … Continue reading
The stable cohomology of SL(F_p)
Back by popular demand: an actual mathematics post! Today’s problem is the following: compute the cohomology of \(\mathrm{SL}(\mathbf{F}_p)\) for a (mod-p) algebraic representation. Step 0 is to say what this problem actually is. It makes sense to talk about certain … Continue reading
Posted in Mathematics, Uncategorized
Tagged completed cohomology, completed K-theory, Eric Friedlander, Evens, K-theory, stable cohomology
4 Comments
Referee Requests
################################################### From: Mathematics Editorial Office Subject: [Mathematics] Review Request Date: December 26, 2018 at 7:43:31 AM CST Dear Professor Calegari, Happy new year. We have received the following manuscript to be considered for publication in Mathematics (http://www.mdpi.com/journal/mathematics/) and kindly invite … Continue reading
Posted in Mathematics, Rant, Uncategorized
Tagged Elsevier, MPDI, Predatory Journals, Reviewing Scam
7 Comments
Local-global compatibility for imaginary quadratic fields
One of the key steps in the 10-author paper is to prove results on local-global compatibility for Galois representations associated to torsion classes. The results proved in that paper, unfortunately, fall well-short of the optimal desired local-global compatibility statement, because … Continue reading
Jacquet-Langlands and an old R=T conjecture
This is part 2 of a series of posts on R=T conjectures for inner forms of GL(2). (See here for part 1). (Edit: this is still incorrect and there should have been a part 3, but I’ve been distracted… in … Continue reading