Tag Archives: Venkatesh

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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Ventotene, Part II

I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading

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Gross Fugue

Here are some variations on the theme of the last post, which is also related to a problem of Dick Gross. In this post, I want to discuss weight one modular forms where the level varies in the “vertical” aspect … Continue reading

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En Passant III

Question: When you are sick in bed, can you do any mathematics? I just spent the past few weeks with a sinus infection and was completely unable to do anything productive, that is, apart from writing an NSF grant (which … Continue reading

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Torsion in the cohomology of co-compact arithmetic lattices

Various authors (including Bergeron and Venkatesh) have shown that the cohomology of certain arithmetic groups have a lot of torsion. For example, if is a co-compact arithmetic lattice in , and is an acyclic local system, then The proof relies … Continue reading

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