Two new pieces of research looked at DNA evidence to try figure out who the Jews are. This has been done before, and the results consistently say what the Jews have been saying all along, though these two new projects seem to be based on broader evidence and techniques. The story, in a nutshell, goes like this:
The Jews came from the Levant (i.e: around here), and they share lots of DNA with local Arabs. The Ethiopian and Indian communities seem furthest out. There was a significant division around 2,500 years, when the Jews of Iran and Iraq seem to have largely broken off from those to their West. (Nebuchadnezzar, anyone?). The Ashkenazim, who lived in Europe from about a thousand years ago, and the Sepharadim, who lived in Southern Europe, North Africa and the Middle East (another name for here), seem to have intermarried more than you might have thought.
There was some intermarriage with the surrounding people all along, but not as much as it would have been reasonable to expect (whatever that means).
The NYT article mentions Shlomo Sand as being wrong, though I don't think he had convinced many Jews anyway, except of course the Mondoweiss camp who were convinced before he ever set pencil to paper, and will remain convinced no matter what contrary evidence is produced.