Open problems

[Harley Eades III <harley.eades@gmail.com>]

Hi, everyone.

Dee Roytenberg’s email pushed me to write an email I have been wanting to write
for a bit.

One thing I have been trying to do recently is figure out what the major (and minor)
open problems are with respect to applications of category theory to CS.   I am very
new to this area, and getting an idea of what folks are working on, and what problems
people feel are important will help young researchers learns where to concentrate 
their efforts.

I am thinking perhaps we could compile a list of research topics/open problems in
this area.  I hope some of the experts who read this mailing list would like to add 
their thoughts.

To start us off here are a few that I know of:

1. Homotopy type theory
     - The study of a new interpretation of intensional type theory based in homotopy 
        theory. This line of research has a lot of interesting problems that need to be
        solved, and as applications in the design and analysis of functional programming 
        languages, and software verification. 

2. Databases
     - David Spivak has done a lot of great work applying category theory to the design
       and analysis of databases.  I am not sure what the current major open problems are.

3. Security
     - Dusko Pavlovic currently has a number of projects related to security that use category
       theory either explicitly or are inspired by categorical concepts.  I have read a few of
       his papers in this line of work, but I am not sure of the current open problems.  A list
       of the papers in this line were posted here awhile ago and can be found here: 
          http://article.gmane.org/gmane.science.mathematics.categories/8068/match=

What other topics or specific open problems do others know about?  

I look forward to hearing about more.

Very best regards,
Harley Eades

 




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