Stir together yeast, water, and sugar in a large bowl, and let stand until foamy, about 5 minutes. Stir in flour, 1/2 teaspoon salt, and the oil until combined. Turn out dough onto a lightly floured surface, and knead with floured hands until smooth, about 2 minutes. Transfer to a large oiled bowl, and cover with plastic wrap. Let stand in a warm, draft-free spot for 20 minutes.
Preheat oven to 400 degrees. Divide dough into quarters. On a lightly floured surface, roll out 1 piece of dough to 8 by 5 inches. Transfer to a baking sheet lined with parchment paper. Repeat with remaining dough. Divide radicchio among flatbread, and gently press into dough. Drizzle with oil; season with salt and pepper. Bake until flatbread is golden and crisp, about 15 minutes.
Whisk ricotta in a small bowl until lightened. Drizzle flatbread with oil; season with salt and pepper. Serve flatbread with ricotta.