- The string topology BV algebra, Hochschild cohomology and the Goldman bracket on surfaces.
Mathematics or mathematical physics don't have to be a financial disaster as long as you stay at the high school. :-) But don't get a false impression here. The money must be used for higher education.
Mitka is looking at Harvard at MIT for further mathematical adventures.
At asymptotia.com, a well-known critic of science has pre-emptively attacked Clifford Johnson and "accused" him and others of the intent to pretend that string topology is a kind of part of string theory. What a crime. ;-)
I happen to think that string topology is indeed a subset of mathematics inspired by and relevant for string theory such as Gromov-Witten theory, topology of moduli spaces and spaces of paths etc. as organized by topological string theory and topological field theory. Why do you think that string topology is called string topology and not quantum graphity topology, among other choices?
Look at a review of string topology and count how many times it talks about D-branes, sigma-model, Witten, Dijkgraaf, and other things. How could it *not* be a part of broader string theory? The degree of irrationality of some people's assertions is simply astonishing.
To see that string topology is a part of the mathematical subcommunity of the broader string theory community, see also this string topology workshop in Stony Brook that defines the subject pretty clearly. The webpage is called "string topology" but it is found in the directory "string theory". Now, your humble correspondent doesn't like to view these things as a rigorous mathematician and he doesn't understand most of these things but he can still recognize that they often study the same structures with a different focus and motivation, with higher standards of rigor, with smaller or no attention to the physical relevance, and with a higher degree of generality than what is useful for physics.
Nevertheless, I am now learning category theory, functors, sheaves, and other things, with the help of Mihail F. - thank you! But my guess is that this mathematical setup will never become the way how I think about problems although it is sometimes tempting.