Permaculture sounds like a really complicated science-y word. While in fact a science, it is also simply the idea of using the nature of plants and animals to sustain one another in a balanced way. The word is a combination of “permanent” and “agriculture” as well as “permanent” culture.
There are many people in the city working with permaculture and its popularity is rising due to the difficulties in the economy and the rising interest in renewable energy and sustainable agriculture. Green roofs, sustainable agriculture and aesthetics of garden design all have a permaculture theme. Because permaculture is a more scientifica and deliberate approach to gardening, its study is even more appealing. Instead of having to tend a garden, permaculturists establish growing areas that can sustain itself either through conservation and sharing of water and resources, or combinations of plants and animals that live/grow symbiotically.
New York City has an active Permaculture Meetup group that offers gardening and permaculture workshops. There is even a certification to be a permaculturist.
Some recommended readings can be found on this site of a highly-regarded permaculturist, Larry Santoyo: http://earthflow.com/books.php
There is also a permaculture wiki that is a vast repository of information.