Heat the oven to 375 degrees with the rack positioned in the center.
Make the topping: whisk the cornmeal, flour, both sugars and salt in a bowl. Toss in the butter. Use your fingers, a fork or pastry blender to blend the butter into the flour mixture until it looks like damp, clumpy sand. Add the almonds and mix briefly to combine.
Put the cherries in another large mixing bowl. Add the lemon juice, almond extract, sugar and cornstarch and stir together.
Put the cherry mixture in a large (11-inch) round baking dish. Distribute the topping over the cherries to cover.
Bake the crisp 35 - 40 minutes. The top should be golden and the juices bubbling.