Lifts of projective congruence groups. (arXiv:0905.4798v1 [math.NT])

... Verrill We show that noncongruence subgroups of SL_2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they... for asking this question is related to modular forms: projectively equivalent groups have the same spaces of cusp forms .... We also develop algorithms that construct all subgroups projectively equivalent to a given congruence subgroup and decides which ...

Teeth and moustaches.

On Tuesday I was walking in my office's lobby on my way to lunch, and I saw a guy in a business suit vomiting into the plants they have growing in there. Not just vomiting, but puking his guts out projectively. I haven't seen puke like that since being at IU. I asked if he wanted some water, but he just shrugged me away. So I went to the cafe in the building and got a glass of water and some ...

... to walk on flat land for a while.   There is no rationale behind why I did it.   All I know is that I did it.   Like word vomit..   I threw up the words forcefully and projectively.   I wanted to swallow it back down, I immediately wanted for this to have never happened.   I immediately begged and longed to walk over the mounds again.   I’ll climb mount everest if it means never feeling ...

counterfactual poeticism

... aren't really the case just because we aren't always involved with the comportments of the 'a'? Well, in a sense, we are involved with those comportments, not insofar as being 'physically there ', but rather projectively there. "The earth is round" has a truth to it despite the fact that to see it as having a ball-shape, one would need to be in outer space, for when we make this proposition ...