Category Archives: Mathematics

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

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Pseudo-representations and the Eisenstein Ideal

Preston Wake is in town, and on Tuesday he gave a talk on his recent joint work with Carl Wang Erickson. Many years ago, Matt and I studied Mazur’s Eisenstein Ideal paper from the perspective of Galois deformation rings. Using … Continue reading

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A non-liftable weight one form modulo p^2

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor 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

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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

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Virtual coherent cohomology

I gave a talk yesterday where I attempted to draw parallels between the cohomology of (arithmetic) 3-manifolds and weight one modular forms. It was natural then to think about whether there was an analogue of the virtual Betti number conjecture. … Continue reading

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The class number 100 problem

Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading

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Central Extensions, Updated

I previously mentioned a problem concerning polynomials, whose motivation came from thinking about weight one forms and the inverse Galois problem for finite subgroups of I still like the polynomial problem, but I realized that I was confused about the … Continue reading

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