Point of fact I never claimed there was at the start of my posts that the byzantines were "modern Greeks" (i did later on and i stand by that to a degree). There is still some debate whether or not the high period of Greek cultural supremacy ended with the roman conquest of Greece or when Constantinople fell, but Greeks as an ethnic group have existed like the Celts of Wales, Scotland and Ireland not to mention Brittany, since antiquity.
http://en.wikipedia.org/wiki/Greeks . Now thats a dump of data but my point there if you care to peruse the data, is the section on survivability of the language, which while adapting to the changes that history has brought,
has not died (id love to underline that to stress my point) and has a written tradition stretching back nearly 3,000 years. The greeks like every other successful ethnic group in the twentieth century, has had intermarriage, but they still exist as a culture and have not died out. There is no break in the genetics or the language, therefore the Greeks of classical antiquity still exist in their descendants, as do the Jews, Celts and Basques.