Tag Archives: Akshay Venkatesh

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 some … Continue reading

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Artin No-Go Lemma

The problem of constructing Galois representations associated to Maass forms with eigenvalue 1/4 is, by now, a fairly notorious problem. The only known strategy, first explained by Carayol, is to first transfer the representation to a unitary group over an … Continue reading

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Derived Langlands

Although it has been in the air for some time, it seems as though ideas from derived algebraic geometry have begun to inform developments in the Langlands program. (A necessary qualifier: I am talking about reciprocity in the classical arithmetic … Continue reading

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Harris 60

I’ve just returned from the excellent MSRI workshop which honored Michael Harris’ 60th birthday, and here is a brief summary of some of the gossip and mathematics I picked up when I was there. First, let me take note of … Continue reading

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The distribution of Hecke eigenvalues, part II

Here are some numbers from KB promised in my last post. “For the first 61595 newforms of squarefree level coprime to 15 here’s the field extension of Z/3Z generated by the field extensions:” Total Number Number of Galois conjugacy classes … Continue reading

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