I was intrigued by the unusual mixture of large and small leaf bundles. I am guessing American Elm, but the bark seems smoother than photos I've seen. This is part of a project to identify the trees of Tompkins Square Park , in NYC's East Village (TSPTIP). This tree is halfway between 7th and 8th streets on the east side of the park. I'll be adding map coordinates via Flickr's system.
Most votes so far are for Hornbeam (Carpinus sp.)
I am a novice in tree identification. Help on terminology etc. is more than welcome.