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Meta
Author Archives: Persiflage
Potential Modularity of K3 surfaces
This post is to report on results of my student Chao Gu who is graduating this (academic) year. If \(A/F\) is an abelian surface, then one can associate to \(A\) a K3 surface \(X\) (the Kummer surface) by blowing up … Continue reading
Posted in Mathematics, Work of my students
Tagged Chao Gu, George Boxer, Morrison, Picard Group, Picard Rank, Stefan Patrikis, Tate Conjecture, Toby Gee, Vincent Pilloni
2 Comments
Peak Hyde Park
Me dressed as a crocodile chasing the Groke while being chased by Drinfeld down Harper Ave on Halloween (all in front of a 16 foot inflatable pumpkin). Sadly, Drinfeld was not dressed as a Shtuka.
The future is now; recap from Cetraro
I’ve just returned from the second Journal of Number Theory biennial conference in Italy. It’s always nice to get a chance to see slices of number theory one wouldn’t otherwise see at the conferences I usually go to (although this … Continue reading
Locally induced representations
Today is a post about work of my student Chengyang Bao. Recall that Lehmer’s conjecture asks whether \(\tau(p) \ne 0\) for all primes \(p\), where \(\Delta = q \prod_{n=1}^{\infty} (1 – q^n)^{24} = \sum \tau(n) q^n\) is Ramanujan’s modular form. … Continue reading
Posted in Mathematics, Students, Work of my students
Tagged Chengyang Bao, Lehmer's Conjecture, Naser Sardari, Swinnerton-Dyer
1 Comment
Joël Bellaïche
Very sad to hear that Joël Bellaïche has just died. He got his PhD at the same time as me, and I first got to know him during the Durham conference in 2004 and later at the eigenvarieties semester at … Continue reading
Posted in Mathematics
Tagged Bloch-Kato, Eigenvarities, Gaëtan Chenevier, Joël Bellaiche, p=/=13
3 Comments
Murphy’s Law for Galois Deformation Rings
Today’s post is about work of my student Andreea Iorga! A theorem of Ozaki from 2011, perhaps not as widely known as expected, says the following: Theorem: Let \(p\) be prime, and let \(G\) be a finite \(p\)-group. Then there … Continue reading
What would Deuring do?
This is an incredibly lazy post, but why not! Matt is running a seminar this quarter on the Weil conjectures. It came up that one possible way to prove the Weil conjectures for elliptic curves over finite fields is to … Continue reading
Posted in Mathematics
Tagged Brian Conrad, Class Field Theory, Hilbert class field, Matthew Emerton, Max Deuring, Weil Conjectures
3 Comments
A random curve over Q
Let \(X/\mathbf{Q}\) be a smooth projective curve. I would like to be able to say that the motive \(M\) associated to \(X\) “generally” determines \(X\). That is, I would like to say it in a talk without feeling like I’m … Continue reading
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