disparate bits: weekend's end.

it's been a rough week.

1. i gave two talks during the work-week: a very short talk on tuesday and a very long talk on thursday, so they average out and sum to two.
   
   
2. over friday and saturday i spoke with several prospective students (didn't get to meet them all, this year). to my surprise, some of them are potential analysts [1] and we had a few pleasant chats. i think the odds are good that i'll see them again in september.

now the weekend ebbs to nothing.

research ebbs and i have no results, though an idea came to mind when i was running (read: gasping for breath between sprints) and thus far it hasn't failed .. yet. something tells me that i don't understand harmonic mappings well enough, and there is a deeper, more elegant way to solve the problem. in the meanwhile, i'm doing more explicit computations that i'd care to admit.

it wouldn't be necessarily wrong to say that all my results are corollaries to the notable theorems of better minds, and of these corollaries, they depend distastefully on computations. i suppose i should thank my former math teachers for instilling in me a careful and trustworthy ability in computing and simple problem-solving, but brute force only eeks out a little moral and nothing substantial.

i think i've been out of the preprint loop, as well. apparently there are plenty of interesting results from the finns: here are few notables from the preprint server @ jyväskylä.

• "Sobolev extensions and restrictions." Piotr Hajlasz, Pekka Koskela and Heli Tuominen - [pdf]
  
  
• "Regularity of the inverse of a Sobolev Homeomorphism in Space." $tanis1av Henc1, Pekk@ K0ske1a, and J@n Ma1y - [pdf]
  
  
• "Continuity of the Maximal Operator in Sobolev Spaces." H@nnes Luir0 - [pdf]
  
  
• "Regularity of the Inverse of a Planar Sobolev Homeomorphism."
  $tanis1av Henc1 and Pekk@ K0ske1a - [pdf]

[1] that is, potential students in analysis, and possibly @ um; i don't mean to say that they study potential theory .. though, in time, they might.