most recent 30 from http://mathoverflow.net 2013-05-21T10:56:59Z http://mathoverflow.net/feeds/user/3889 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22619/perverse-sheaves-macpherson-lecture-notes/22649#22649 Tom Braden 2010-04-26T21:28:01Z 2010-04-27T11:40:05Z

<p>The notes on Friedman's page are great -- they were very helpful when I was learning about perverse sheaves as a graduate student, since they explain how to think about middle perversity perverse sheaves on complex analytic spaces with complex stratifications (the case of most interest for most people) without having to first define the derived category. Unfortunately the main result there, although it is a theorem, is not fully proved in the notes. One of Bob's students, Mikhail Grinberg, had a project to fill in the details and flesh out the notes into a book, but he left mathematics for a job at Renaissance Technologies. He taught a course at MIT around 2000 where he went through the steps needed to fill in the proof. Perhaps someone has usable notes from that class?</p> <p>The 1993 course was quite different. Again the goal was to see perverse sheaves and their abelian category structure without going through the derived category, but he was working with arbitrary perversities on a regular cell complex. By putting weird "phantom dimensions" on the cells and putting arrows between cells of adjacent phantom dimensions you get a quiver whose representations are perverse sheaves constructible for the cell complex structure. But it's hard to use this to compute beyond simple examples, because the cell complexes would have to be very large, and it's hard to define the condition that gives constructibility for a coarser stratification like a complex analytic one.</p>

http://mathoverflow.net/questions/19046/open-source-mathematical-software/19051#19051 Tom Braden 2010-07-25T13:32:30Z 2010-07-25T13:32:30Z

Polymake (<a href="http://www.opt.tu-darmstadt.de/polymake/doku.php/start" rel="nofollow">opt.tu-darmstadt.de/polymake/doku.php/start</a>) is a system for studying convex polytopes and related objects such as fans and simplicial complexes.

http://mathoverflow.net/questions/2147/most-helpful-math-resources-on-the-web/2236#2236 Tom Braden 2010-06-18T12:43:14Z 2010-06-18T12:43:14Z

Finding forward and back references is indeed one of the most amazing and useful things about MathSciNet, but be aware that not everything will show up. Articles collected in books and older articles don't have their references in the database. The cutoff seems to be around 2000, but it may be different for different journals.

http://mathoverflow.net/questions/22619/perverse-sheaves-macpherson-lecture-notes/22649#22649 Tom Braden 2010-05-06T17:24:40Z 2010-05-06T17:24:40Z

Besides the papers of Vybornov and Polishchuk, which you've already seen, I don't know another place where those ideas have appeared.